In this paper, we investigate the effects of certain variants of the commutative laws on properties of several families of algebras which are in general not commutative, such as groups, linear algebras, or actually quite anti-commutative, such as $BCK$-algebras and $d$-algebras among others. From results obtained it becomes clear that by considering these variants in the presence of yet other axioms it is to be expected that a quite rich and varied set of results may be obtained both in the general and the particular setting of which what has been accomplished in this paper is a substantial sample.

In this paper, we observe that if X is a set and (Bin(X), □) is the semigroup of binary systems on X, then its center ZBin(X) consists of the locally-zero-semigroups and that these can be modeled as (simple) graphs and conversely. Using this device we show that we may obtain many results of interest concerning groupoids by reinterpreting graph theoretical properties and at the same time results on graphs G may be obtained by considering them as elements of centers of the semigroups of binary systems (Bin(X), □) where X = V(G), the vertex set of G.

If an algebra of type $A$ contains a subalgebra which is also an algebra of type $B$, then it is a Smarandache $B$-type $A$-algebra provided the subalgebra of type $B$ contains at least two elements. This generalizes the notion of Smarandache group, where the group of order $\geq 2$ is a subsemigroup of a semigroup. In this paper we investigate a number of such pairings and we deduce a number of conclusions as a consequence.

In this paper any superalgebra is generalized to a new form, namely ultra algebra. We study some algebraic structure results for ultra algebras and we have defined some maps on ultra algebras to know ultra derivation and Jordan ultra derivation. Moreover on certain assumptions we have proved that Jordan ultra derivation is an ultra derivation.

Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for Novikov coalgebras and the Kantor construction for Jordan super-coalgebras are given. We give examples of a non-locally finite differential coalgebra, Novikov coalgebra, Lie coalgebra, Jordan super-coalgebra, and right-alternative coalgebra. The dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite dimensional simple differential coalgebra, Novikov coalgebra, Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.

Let $(A,\Delta)$ be a {\it weak multiplier Hopf algebra} as introduced in [VD-W3] (see also [VD-W2]). It is a pair of a non-degenerate algebra $A$, with or without identity, and a coproduct $\Delta$ on $A$, satisfying certain properties. If the algebra has an identity and the coproduct is unital, then we have a Hopf algebra. If the algebra has no identity, but if the coproduct is non-degenerate (which is the equivalent of being unital if the algebra has an identity), then the pair would be a multiplier Hopf algebra. If the algebra has an identity, but the coproduct is not unital, we have a weak Hopf algebra. In the general case, we neither assume $A$ to have an identity nor do we assume $\Delta$ to be non-degenerate and so we work with a {\it genuine} weak multiplier Hopf algebra. It is called {\it regular} if its antipode is a bijective map from $A$ to itself. \snl In this paper, we {\it continue the study of weak multiplier Hopf algebras}. We recall the notions of the source and target maps $\varepsilon_s$ and $\varepsilon_t$, as well as of the source and target algebras. Then we investigate these objects further. Among other things, we show that the canonical idempotent $E$ (which is eventually $\Delta(1)$) belongs to the multiplier algebra $M(B\ot C)$ where $B=\varepsilon_s(A)$ and $C=\varepsilon_t(A)$ and that it is a {\it separability idempotent} (as studied in [VD4.v2]). If the weak multiplier Hopf algebra is regular, then also $E$ is a {\it regular} separability idempotent. \snl We also consider {\it special cases and examples} in this paper. In particular, we see how for any weak multiplier Hopf algebra $(A,\Delta)$, it is possible to make $C\ot B$ (with $B$ and $C$ as above) into a new weak multiplier Hopf algebra. In a sense, it forgets the 'Hopf algebra part' of the original weak multiplier Hopf algebra and only remembers the source and target algebras. It is in turn generalized to the case of any pair of non-degenerate algebras $B$ and $C$ with a separability idempotent $E\in M(B\ot C)$. We get another example using this theory associated to any discrete quantum group (a multiplier Hopf algebra of discrete type with a normalized cointegral). Finally we also consider the well-known 'quantization' of the groupoid that comes from an action of a group on a set. All these constructions provide interesting new examples of weak multiplier Hopf algebras (that are not weak Hopf algebras).

We present set-theoretical solutions of the Yang-Baxter equation in BCK–algebras. Some solutions in BCK−algebras are not solutions in other structures (such as MV −algebras). Related to our investigations we also consider some new structures: Boolean coalgebras and a unified braid condition – quantum Yang-Baxter equation. Finally, we will see how poetry has accompanied the development / history of the Yang–Baxter equation.

This dissertation is a rigorous study of ecology and macrocellular biology as a subfield of abstract algebra. We begin with the creation of an axiomatic paradigm, then move onto constructing a universal genetic code of biology. We use this to define increasingly complex algebraic structures (ecosystem, evolving populations, etc.). We prove a variety of theorems regarding to the members of the previous mathematical constructs, notably the following three: 1. There is one unique phenotypic representation of each organism. For example, if you subdivide any piece of genetic code into its phenotypic components, then two identical organisms have identical decomposed DNA 2. There are a finite number of indivisible phenotypic traits. 3. The three sophioid-definitions are equivalent: (a) dynamical evolutionary enlargement of the medial temporal lobe and frontal lobe, (b) reliance upon intelligence, (c) the existence of an intellectually- or socially-hierarchical society. Much has yet to be done on this work, but as a first draft, it stands as a jumping point for future exploits; I am working on an entirely revised second draft.

We propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

In this paper we propose the notion of a transposed Poisson superalgebra. We prove that a transposed Poisson superalgebra can be constructed by means of a commutative associative superalgebra and an even degree derivation of this algebra. Making use of this we construct two examples of transposed Poisson superalgebra. One of them is the graded differential algebra of differential forms on a smooth finite dimensional manifold, where we use the Lie derivative as an even degree derivation. The second example is the commutative superalgebra of basic fields of the quantum Yang-Mills theory, where we use the BRST-supersymmetry as an even degree derivation to define a graded Lie bracket. We prove several identities, which hold in a transposed Poisson superalgebra.

Let N = N₀+ N₁+ N₂ be a Z₃-graded Novikov algebra. The main goal of the paper is to prove that over a field of characteristic not equal to 3 the algebra N is solvable if N₀ is solvable. We also show that a $Z_2$-graded Novikov algebra N=N₀+ N₂ over a field of characteristic not equal to 2 is solvable if N₀ is solvable. This implies that for every n of the form n=2^k3^l, any Z_n-graded Novikov algebra N over a field of characteristic not equal to 2,3 is solvable if N₀ is solvable.

Lie algebra plays an important role in the study of singularity theory and other field of sciences. Finding numerous invariants linked with isolated singularities is always a main interest in the classification theory of isolated singularities. Any Lie algebra that characterizes simple singularity produces a natural question. The study of properties such as to find the dimensions of newly defined algebra is a remarkable work. Hussain, Yau and Zuo \cite{HYZ10} have been found a new class of Lie algebra \texorpdfstring{ $ \mathcal{L}_ k (V)$}{LG}, \texorpdfstring{$k\geq 1$}{LG} i.e., Der ($M_{k}(V), M_{k}(V)$) and purposed a conjecture over its dimension $\delta_{k}(V)$ for $k\geq0$. Later they proved it true for $k$ up to $k=1,2,3,4,5$. In this work, the main concern is whether it's true for a higher value of $k$. According to this, we calculate first, the dimension of Lie algebra \texorpdfstring{$\mathcal{L}_ k (V)$}{LG} for $k=6$ and then compute the upper estimate conjecture of fewnomial isolated singularities. Along with, we also justify the inequality conjecture: \texorpdfstring{$\delta_{k+1}(V) < \delta_{k}(V)$}{LG} for $k=6$. Our calculated results are innovative and a new addition to the study of singularity theory.

We revise the definition of graph operations in [WDK2018] and adapt correspondingly the construction of graph term algebras. As a first contribution to a prospective research field Universal Graph Algebra, we generalize some basic concepts and results from algebras to graph algebras. To tackle this generalization task, we revise and reformulate traditional set-theoretic definitions, constructions and proofs in Universal Algebra by means of more category-theoretic concepts and constructions. Especially, we generalize the concept generated subalgebra and prove that all monomorphic homomorphisms between graph algebras are regular. Derived graph operations are the other main topic. After an in depth analysis of terms as representations of derived operations in traditional algebras, we identify three basic mechanisms to construct new graph operations out of given ones: parallel composition, instantiation, and sequential composition. As a counterpart of terms, we introduce graph operation expressions with a structure as close as possible to the structure of terms. We show that the three mechanisms allow us to construct for any graph operation expression a corresponding derived graph operation in any graph algebra.

We construct families of ground state representations of the U(1)-current net and of the Virasoro nets Vir_c with central charge c ≥ 1. We show that these representations are not covariant with respect to the original dilations, and those on the U(1)-current net are not solitonic. Furthermore, by going to the dual net of with respect to the ground state representations of Vir_c, one obtains possibly new family of Möbius covariant nets on S¹.

The aim of this paper is to show how the mathematical basis is used for a precise treatment of double-entry bookkeeping, which was firstly developed in the nineteenth century by Sir William Rowan Hamilton. This is done by using basic notions of matrix algebra with the roots to the idea of using ordered pairs. We also reveal how the complex numbers and the rationals (fractions) developed in a mainstream of accounting science and became a leading platform for the ongoing processes within the Industry 4.0. The paper concludes with the examples on how accounting operations can be represented by matrix equations with a result of the essential report generating. The author represents a mathematical model of accounting which is independent of the specific existential forms but is capable to undertake the form of any of them and thus has the prospect of being understood and accepted by specialists globally.

The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory, in terms of states as linear functional defined on category algebras. We clarify that category algebras can be considered as generalized matrix algebras and that the notions of state on category as linear functional defined on category algebra turns out to be a conceptual generalization of probability measures on sets as discrete categories. Moreover, by establishing a generalization of famous GNS (Gelfand-Naimark-Segal) construction, we obtain a representation of category algebras of †-categories on certain generalized Hilbert spaces which we call semi-Hilbert modules over rigs.

Let $n \geq 2$ be a fixed integer and $\mathcal{A}$ be a $C^*$-algebra. A permuting $ n $-linear map $ \mathcal{G} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ is known to be symmetric generalized $n$-derivation if there exists a symmetric $n$-derivation $ \mathfrak{D} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ such that $ \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i} x_{i}^{\prime}, \ldots, x_{n}\right)= \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i}, \ldots, x_{n}\right) x_{i}^{\prime}+x_{i} \mathfrak{D} (x_{1}, x_{2},\ldots, x_{i}^{\prime}, \ldots, x_{n})$ holds for all $x_{i}, x_{i}^{\prime} \in \mathcal{A} $. In this paper, we investigate the structure of $C^*$-algebras involving generalized linear $n$-derivations. Moreover, we describe the forms of traces of linear $n$-derivations satisfying certain functional identity.

This paper presents the symmetries of differential equations associated with one-variable and Bivariate Hermite polynomials by proposing a representation of Lie algebra for these differential operators. Applying the Baker-Campbell-Hausdorff formula to these algebras, results in new relations and generating functions in one-variable and Bivariate Hermite polynomials. A general form of representation for other orthogonal polynomials such as Laguerre polynomials is introduced.

In this note we consolidate and give a brief description of several recently published results in ring theory having disproof. These results have been published during 2016 to 2021 in the so called non-predatory reputed mathematical journals indexed in the well known database like Scopus. We have considered results on rings in which each element is a sum of two idempotents appeared in Canad. Math. Bull. (2016), weakly tripotent rings appeared in Bull. Korean Math. Soc. (2018) and Rendiconti Sem. Mat. Univ. Pol. Torino (2021), involution t-clean rings appeared in Eur. J. Pure Appl. Math (2022) and strongly 2-nil clean rings with units of order two appeared in Eur. J. Pure Appl. Math (2023).

As a new approach, for a nonzero normed algebra $A$, we will define some different classes of algebra fuzzy norms on $A$ generated by homomorphisms and continuous homomorphisms. Also as a source of examples and counterexamples in the field of fuzzy normed algebras, separate continuity of the elements of each class are investigated.

We define a spinor-Minkowski metric for SL(4,C). It is not a trivial generalization of the SL(2,C) metric and it involves the Minkowskian one. We define 4x4 version of the Pauli matrices and eight 4-component associated generalized eigenvectors that can be regarded as undotted covariant spinors. The 4-component spinors can be grouped into four categories. Each category transforms in its own way. The outer products of pairwise combinations of 4-component spinors can be associated with 4-vectors. Including the dotted covariant, undotted and dotted contravariant forms totally we have sixteen pairs of spinors. Eight of them live in the conjugate space which has no countepart in SL(2,C).

In this note we introduce the notion of polynions and discuss their mathematical relevance. We note that the well-known mathematical structures like quaternions, octonions and sedenions etc. are special cases of polynions.

The aim of this single-center, open-label, non-controlled randomized study was to evaluate which formulation of vitamin D between cholecalciferol and calcifediol is most effective in the treatment of hypovitaminosis D in older adults. Demographic characteristics, clinical history and comprehensive geriatric assessment were recorded at admission. Eligible patients randomly received an equivalent vitamin D supplement either with cholecalciferol or calcifediol from hospital admission to three months after discharge. Among the 140 older patients included (mean age 83±6.6, 57.8% females), 69 received cholecalciferol and 71 calcifediol. The mean plasma values of 25OH-Vitamin D3 found at the enrollment were 16.8 ± 9.9 ng/mL in patients receiving cholecalciferol and 18.8 ± 13.3 ng/mL in those treated with calcifediol (p =0.31). At the 3-month follow up, the mean concentration of 25OH-Vitamin D3 was significantly higher in patients treated with calcifediol than in patients treated with cholecalciferol (respectively, 30.7 ± 8.4 vs 45.4 ± 9.8 ng/mL, p &lt;0.001). Supplementation with cholecalciferol or calcifediol results in both cases effective in reaching optimal circulating values of 25OH-VitaminD3 in the older patients suffering from hypovitaminosis D. However, supplementation with calcifediol led to average circulating values of 25OH- VitaminD3 significantly higher (over 50%) than those obtained with cholecalciferol.

Vitamin D plays an essential role in embryogenesis and the course of intra- and postnatal periods and is crucially involved in the functioning of the mother-placenta-fetus system. Low quantity of Vitamin D during pregnancy can lead to the elevated risk for preeclampsia occurence. Despite the numerous studies on the association of Vitamin D deficiency and preeclampsia development, the current research on this theme is contradictory. In this review we summarize and analyze study data on the effects of vitamin D deficiency and supplementation on pregnancy, labor, fetal and neonatal outcomes.

This work addresses the problem of automatic head pose estimation and its application in 3D gaze estimation using low quality RGB--D sensors without any subject cooperation or manual intervention. The previous works on 3D head pose estimation using RGB--D sensors require either an offline step for supervised learning or 3D head model construction which may require manual intervention or subject cooperation for complete head model reconstruction. In this paper, we propose a 3D pose estimator based on low quality depth data, which is not limited by any of the aforementioned steps. Instead, the proposed technique relies on modeling the subject's face in 3--D rather than the complete head, which in turn, relaxes all of the constraints with the previous works. The proposed method is robust, highly accurate and fully automatic. Moreover, it does not need any offline step. Unlike some of the previous works, the method only uses depth data for pose estimation. The experimental results on the Biwi head pose database confirm the efficiency of our algorithm in handling large pose variations and partial occlusion. We also evaluate the performance of our algorithm on IDIAP database for 3D head pose and eye gaze estimation.

In this paper, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area and volume, and unifies the calculus of scalar, spinor, vector and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and generalizes real number, complex, quaternion and vector algebra, converts complicated relations and operations into intuitive matrix algebra independent of coordinate systems. By localizing the basis or frame of space-time and introducing differential and connection operators, Clifford algebra also contains Riemann geometry. Clifford algebra provides a unified, standard, elegant and open language and tools for numerous complicated mathematical and physical theories. Clifford algebra calculus is an arithmetic-like operation that can be well understood by everyone. This feature is very useful for teaching purposes, and popularizing Clifford algebra in high schools and universities will greatly improve the efficiency of students to learn fundamental knowledge of mathematics and physics. So Clifford algebra can be expected to complete a new big synthesis of scientific knowledge.

Background: According to newly published studies, patients with Coronavirus Disease 2019 (COVID-19) have significantly lower serum 25-hydroxyvitamin D 25(OH)D levels than those without the SARS-CoV-2 infection. Vitamin D insufficiency may be a predictor of poor prognosis in COVID-19 patients. Vitamin D supplementation is related to improved clinical outcomes in terms of intensive care unit (ICU) admission and death, particularly in individuals with moderate-to-severe forms of COVID-19 requiring hospitalization. Materials and methods: This placebo-controlled five-day study was performed on 100 hospitalized COVID-19 patients with vitamin D insufficiency randomized into two groups. Vitamin D in the form of a sublingual sprayable microemulsion (LYL love your life® sunD3 LYLmicro™) was given three times daily after breakfast, lunch, and dinner (daily dose 12,000 IU) to 52 patients with blood vitamin D levels below 30 ng/ml. 48 patients in the control group received a placebo spray in the same daily regiment. Results: We observed a statistically significant increase by 8.6 ng/ml in median vitamin D level after five days of high-dose vitamin D3 spray therapy. 90.2% of subjects reached normal serum levels of vitamin D. There was a strong correlation between changes in vitamin D and C-reactive protein (CRP) levels in individuals with moderately severe disease (p<0.05), while mild and severe cases showed no statistical significance comparing case and control groups. There were no statistically significant changes in ferritin and interleukin-6 (IL-6) levels. Conclusions: In this study, we demonstrated the possibility to rapidly increase circulating levels of vitamin D just in 5 days of high-dose intervention and found a statistically significant decrease of CRP levels in patients with moderately severe COVID-19. We were not able to detect statistically significant changes in ferritin and IL-6 levels during the 5-day vitamin D intervention.

Vitamin D, unlike the micronutrients, vitamins A, E and K, is largely obtained, not from food, but by the action of solar UV light on its precursor, 7-dehydrocholesterol, in skin. With the decline in UV light intensity in winter, most skin production of vitamin D occurs in summer. Because no defined storage organ or tissue has been found for vitamin D, it has been assumed that adequate vitamin D status in winter can only be maintained by oral supplementation. Skeletal muscle cells have now been shown to incorporate the vitamin D-binding protein (DBP) from blood into the cell cytoplasm where it binds to cytoplasmic actin. This intracellular DBP provides an array of specific binding sites for 25-hydroxyvitamin D (25(OH)D) which diffuses into the cell from the extracellular fluid. When intracellular DBP undergoes proteolytic breakdown, the bound 25(OH)D is then released and diffuses back into blood. This uptake and release of 25(OH)D by muscle, accounts for the very long half-life of this metabolite in the circulation. As 25(OH)D concentration in blood declines in winter, its cycling in and out of muscle cells appears to be upregulated. Parathyroid hormone is the most likely factor enhancing the repeated cycling of 25(OH)D between skeletal muscle and blood. This mechanism appears to have evolved to maintain adequate vitamin D status in winter.

Vitamin D, unlike the micronutrients, vitamins A, E and K, is largely obtained, not from food, but by the action of solar UV light on its precursor, 7-dehydrocholesterol, in skin. With the decline in UV light intensity in winter, most skin production of vitamin D occurs in summer. Because no defined storage organ or tissue has been found for vitamin D, it has been assumed that adequate vitamin D status in winter can only be maintained by oral supplementation. Skeletal muscle cells have now been shown to incorporate the vitamin D-binding protein (DBP) from blood into the cell cytoplasm where it binds to cytoplasmic actin. This intracellular DBP provides an array of specific binding sites for 25-hydroxyvitamin D (25(OH)D) which diffuses into the cell from the extracellular fluid. When intracellular DBP undergoes proteolytic breakdown, the bound 25(OH)D is then released and diffuses back into blood. This uptake and release of 25(OH)D by muscle, accounts for the very long half-life of this metabolite in the circulation. As 25(OH)D concentration in blood declines in winter, its cycling in and out of muscle cells appears to be upregulated. Parathyroid hormone is the most likely factor enhancing the repeated cycling of 25(OH)D between skeletal muscle and blood. This mechanism appears to have evolved to maintain adequate vitamin D status in winter.

1) Background: The aim was to evaluate the bioefficacy of vitamin D (VitD) encapsulated in nanoemulsions developed by sonication and pH-shifting of pea protein isolate in restoring VitD status in VitD-deficient rats. 2) Methods: Weaned (3-week old), male albino rats (n = 35) were initially divided into two groups: control sufficient group (VDS; n = 7) fed on a normal AIN-93G diet and a VitD-deficient group (n = 28) fed a VitD-deficient diet for six weeks. VitD-deficient rats were divided into four subgroups: two treatment groups (Nano+VitD and Oil+VitD) and two control groups (Nano-VitD and Oil-VitD), receiving seven rats in each sub-group. Nano+VitD and Oil+VitD groups received VitD dispersed in PPI-nanoemulsions and in canola oil, respectively, while the control groups received the respective delivery vehicles without VitD. Serum 25-hydroxyvitamin D [25(OH)VitD], parathyroid hormone (PTH), calcium (Ca), phosphorus levels (P), and alkaline phosphatase (ALP) activity were measured. Femur bone was used to prepare histopathological sections. 3) Results: After one week of treatment, the VitD-deficient rats consuming Nano+VitD recovered from VitD deficiency (serum 25(OH)VitD 34.38 ± 7.00) compared to the sufficient control (36.84 ± 9.16; p > 0.05) and the deficient control consuming VitD+Oil (14.05 ± 3.08; p < 0.01). Enhancement in VitD status was followed with expected changes in serum PTH, Ca, P, and ALP levels, no difference in similar biomarkers against the sufficient control, and an improvement of the osteoid area and reduction of trabecular separation in bone. 4) Conclusions: Stabilization of VitD within PPI-based nanoemulsions enhances its absorption and restores its status and biomarkers of bone resorption in VitD-deficient rats.

Vitamin D (VD) is a pro-hormone essential for life in higher animals. It is present in few types of foods and is produced endogenously in the skin by a photochemical reaction. The final step of VD activation occurs in the kidneys involving a second hydroxylation reaction to generate the biologically active metabolite 1,25(OH)₂-VD. Extrarenal 1α-hydroxylation has also been described to have an important role in autocrine and paracrine signaling. Vitamin D deficiency (VDD) has been in the spotlight as a major public health-care issue with an estimated prevalence of more than a billion people worldwide. Among individuals with chronic kidney disease (CKD), VDD prevalence has been reported to be as high as 80%. Classically VD plays a pivotal role in calcium and phosphorus homeostasis. Nevertheless, there is a growing body of evidence supporting the importance of VD in many vital nonskeletal biological processes such as endothelial function, renin-angiotensin-aldosterone system modulation, redox balance and innate and adaptive immunity. In individuals with CKD, VDD has been associated with albuminuria, faster progression of kidney disease and increased all-cause mortality. Recent guidelines support VD supplementation in CKD based on extrapolation from cohorts conducted in the general population. In this review, we discuss new insights on the multifactorial pathophysiology of VDD in CKD as well as how it may negatively modulate different organs and systems. We also critically review the latest evidence and controversies of VD monitoring and supplementation in CKD patients.

Vitamin D status may impact acute affective symptomatology and the severity of symptoms in patients with bipolar disorder (BD). Therefore, this cross-sectional study analyzed 25(OH)D, 24,25(OH)2D, and the vitamin D metabolite ratio (VMR) in BD and correlated the results with clinical affective symptomatology and functionality. The inactive precursor 25(OH)D and its principal catabolite 24,25(OH)2D were measured simultaneously with a validated liquid chromatography tandem mass-spectrometry method in 170 BD outpatients and 138 healthy controls. VMR was calculated as follows: VMR=100*(24,25(OH)2D/25(OH)D). The psychometric assessment enclosed: Beck Depression Inventory-II, Hamilton Depression Rating Scale, Young Mania Rating Scale, Global Assessment of Functioning, and number of suicide attempts. We did not find a significant difference between patients and controls in the concentrations of 25(OH)D and 24,25(OH)2D. Additionally, the VMR was comparable in both groups. The calculations for the clinical parameters showed a negative correlation between the Young Mania Rating Scale and 24,25(OH)2D (r = -.154, p = .040). Based on the small effect size and the predominantly euthymic sample, further exploitation in individuals with manic symptoms would be needed to confirm this association. In addition, long-term clinical markers, and an assessment in different phases of the disease may provide available additional insights.

(1) Background: Many malignancies are driven by mutations which affect the gene for fibroblast growth factor receptor (FGFR) 1. Previously we have documented that signal transduction from FOP2–FGFR1 fusion protein in KG1 cells downregulated the expression of vitamin D receptor (VDR) gene. In this paper we investigated if also other FGFRs were responsible for the regulation of the VDR expression. (2) Methods: We used human myeloid leukemia cells U937, and bone cancer cell line U2OS, and cell transfection methods in order to address the above questions. (3) Results: In myeloid leukemia cells overexpression of FGFR 1-4 caused shift to granulocytic differentiation, upregulated expression of VDR, and sensitized these cells to 1,25-dihydroxyvitamin D (1,25D)-induced monocytic differentiation, while in bone cells, signal transduction activated by FGF1 was not responsible for regulation of VDR expression and activity. (4) Conclusions: Since the overexpression of FGFRs occurs in many neoplasms, it may be reasonable to use 1,25D analogs in these cancers, in which overexpression of FGFRs leads to VDR upregulation.

The role of vitamin D in the prevention and treatment of non-skeletal health issues has received significant media and research attention in recent years. Costs associated with clinical management of low vitamin D (LVD) have increased exponentially. However, no clear evidence supports vitamin D screening to improve health outcomes. Authoritative bodies and professional societies recommend against population-wide vitamin D screening in community-dwelling adults who are asymptomatic or at low risk of LVD. In order to assess patterns of physician management of LVD in this conflicting environment, we conducted a scoping review of three electronic databases and gray literature. Thirty-eight records met inclusion criteria and were summarized in an evidence table. Results from seven countries showed a consistent increase in vitamin D lab tests and related costs. Many vitamin D testing patterns reflected screening rather than targeted testing for individuals at high risk of vitamin D deficiency or insufficiency. Interventions aimed at managing inappropriate clinical practices related to LVD were effective in the short term. Variability and controversy were pervasive in many aspects of vitamin D management, shining light on physician practices in the face of uncertainty. Future research is needed is needed to inform better clinical guidelines and to assess implementation practices that encourage evidence-based management of LVD in adult populations.

An image consisting of (m, n) pixels can be seen as a matrix of m × n size. Based on the formula of angles between two subspaces, a pair of angles can be defined between two matrices, by utilizing column spaces and row spaces of the two matrices. The singular values of each matrix can be used to calculate distances. Thus, a distance representation is obtained, and a pair of angles between 2 matrices of the same size.

Steganography is the branch of cryptology that deals with concealing information inside another information. it’s prefer over cryptography as it hides a message inside another innocent looking message, while cryptography shows scrambled message that might arouse attention of an attacker, however the challenges in steganography is the modification of carrier that causes some abnormalities which is detectable and often the methods are not optimize. This paper presents a novel approach in cryptography and steganography, which utilizes mathematical concept of bits combination to optimize time of transmission using sets of multiple transmitter, and receiver’s addresses where each abstractly represents a bits combination without itself modified. In addition, the paper introduces a concept of dynamical clockwise and anti-clockwise rotation of bits combination over addresses after every transmission to reinforce resistivity against steganalysis.

The aim of this article is introduced the concept of double framed T-soft fuzzy set (DFT-soft fuzzy set) which is the combination of soft set and fuzzy set. We also defined the notions and apply this concept in BCK/BCI-algebras. By using example, we also discussed the concept of double framed T-soft fuzzy algebra (DFT-soft fuzzy algebra) and double framed B-soft fuzzy algebra (DFB-soft fuzzy algebra) and also investigated their properties. Each double framed T-soft fuzzy algebra is double framed B-soft fuzzy algebra but by using example, we proved that converse may or may not be possible.

Severe infection from the SARS-CoV-2 virus is associated with various clinical findings, including hematological manifestations. Thrombotic events or a tendency to develop thrombotic events also characterize severe COVID-19 disease and may lead to death. Vitamin D is known to have immunomodulating properties and to enhance the body defense system against invading pathogens and to have immunostimulatory properties as far as the innate immune response is concerned. The aim was to measure 25(OH)D3 levels in patients hospitalized for severe COVID-19 infection, to explore the relationship between 25(OH)D3 and outcome and to investigate the relationship between 25(OH)D3 levels, CRP, ferritin, d-dimers and fibrinogen levels in this cohort. In a cohort of 88 patients hospitalized for severe infection from the SARS-CoV-2 virus and a control group matched for age and sex the levels of 25(OH)D3 were measured. In the same cohort CRP, ferritin, d-dimer and fibrinogen levels were also analyzed. Levels of 25(OH)D3 were 17.36±8.80 ng/ml (mean±SD) as compared with 24.34±10.34 ng/ml, in patients with severe SARS-CoV-2 infection and the control group, respectively, p<0.001 (Student’s t test). The levels of 25(OH)D3 were found to be significantly related to outcome, i.e. survival as opposed to non-survival, as more patients with 25(OH)D3 deficiency (0-10 ng/ml) and insufficiency (10-20 ng/ml) had a fatal outcome as compared with those with vitamin D sufficiency, p<0.001, chi-square test, p<0.001, Fischer’s exact test. Levels of 25(OH)D3 were inversely related to CRP, ferritin, d-dimer and fibrinogen levels, p<0.001, linear regression analysis, beta coefficient of variation, -0.176, -0,160, -0.178, -0.158, respectively. Vitamin D deficiency observed in severe SARS-CoV-2 infection was related to the disease outcome. Increased ferritin levels, and increased thrombotic markers, namely d-dimer and fibrinogen levels were observed in the patients and their concentration was also inversely related to vitamin D. We showed that vitamin D levels were low in hospitalized patients with severe SARS-CoV-2 infection and also inversely related to CRP, ferritin, d-dimer and fibrinogen concentration. It is proposed that vitamin D levels may be an index of severity in the context of SARS-CoV-2 infection.

(1) Background: To investigate the effect of phosphohistone H3 (PHH3) and vitamin D receptor (VDR) in the risk assessment of endometriosis, in two cohorts of women with this pathology, those receiving hormonal treatment, and those without treatment; (2) Methods: In 60 cases of women with endometriosis, the paraffin-embedded endometriosis tissue samples, retrieved after surgery, were immunohistochemically (IHC) analyzed aiming to determine the expression status of PHH3 and VDR; (3) Results: The IHC positive index of PHH3 and VDR of these two groups were compared. PHH3 levels were positively correlated with vitamin D levels, both being increased in patients without treatment. Within the group without treatment, PHH3 and VDR expressions were positively associated; (4) Conclusions: IHC analysis of PHH3 and VDR can be used as an additional tool for risk stratification and prognostic assessment in patients with endometriosis.

This article is the first part of a scientific project under the general title "Geometrized Vacuum Physics". This study is based on two main postulates: 1) independence of the propagation velocity of electromagnetic waves in vacuum from their frequency; 2) the constancy of the averaged zero vacuum balance, associated with the assertion that only mutually opposite formations are born from vacuum, so that on average they completely compensate for each other's manifestations. In this part of the "Geometrized Vacuum Physics" the foundations of the Algebra of Stignatures are laid, which is the mathematical and logical foundation of the entire project. In the next articles of this project it will be shown that the Algebra of Stignatures can be used for the development of "zero" (vacuum) technologies, algebraic genetics, vacuum cosmology, the vacuum standard model of "elementary particles", vacuum gravity and levitation, vacuum energy, ethics and aesthetics and many other branches of knowledge. At the end of this article, one of the many possible applications of the Algebra of Stignatures is given, in particular, the basics of the stignature-spectral analysis are outlined, with the help of which the possibilities of communication channels can be significantly expanded.

Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This algebra shows the standard operation procedure and deep insights into the structure of the equations. Usually, the integrable condition is related to the special symmetry of transformation group, which involves some advanced mathematical tools and its availability is limited. In this paper, the integrable conditions are only regarded as algebraic conditions. The commutators expressed by Clifford algebra have a neat and covariant form, which are naturally valid in curvilinear coordinate system and curved space-time. For Pauli and Schr\"odinger equation, many solutions in axisymmetric potential and magnetic field are also integrable. We get the scalar eigen equation in dipole magnetic field. By the virtue of Clifford algebra, the physical researches may be greatly promoted.

We investigate and discuss in detail the structure of the restricted singular value decomposition for a tensor triplet under t-product (T-RSVD). The algorithm is provided with a numerical example illustrating the main result. For applications, we consider color image watermarking processing with T-RSVD.

This article is the second part of a scientific project under the general name "Geometrized vacuum physics". On the basis of the Algebra of Stignatures presented in the previous article [1], this article develops the main provisions of the Algebra of Signatures. Both of the above algebras are aimed at studying the properties of an ideal vacuum, but at the same time they are universal and can be applied in various branches of knowledge. It is shown that the signature of a quadratic form is related to the topology of the metric space for which the given quadratic form is a metric. Conditions are given under which an additive imposition of metric spaces with different topologies (or signatures) leads to a total Ricci flat space similar to a Calabi-Yau manifold. A spin-tensor representation of metrics with different signatures is considered and a Dirac bundle of quadratic forms is presented. This article does not contain physical applications of the Algebra of Signatures, but the potential power of this mathematical apparatus will be demonstrated in subsequent articles of this project.

We develop the theory of Heyting small spaces and prove a new version of Esakia duality for such spaces. To do this, we notice that spectral spaces may be seen as sober small spaces with all smops compact and introduce the method of the standard spectralification. This helps to understand open continuous definable mappings between definable spaces over o-minimal structures.

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1+1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1+2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1+2 dimensions.

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. We find two classes of representation, the normal representation and exceptional one. The normal representation is a large class of representation which can only be expanded into $4m+1$ dimension, but the exceptional representation can be expanded as generators of the next period. In the cases $p+q=4m$, the representation is unique in equivalent sense. These results are helpful for both theoretical analysis and practical calculation. The generators of Clifford algebra are the faithful basis of $p+q$ dimensional Minkowski space-time or Riemann space, and Clifford algebra converts the complicated relations in geometry into simple and concise algebraic operations, so the Riemann geometry expressed in Clifford algebra will be much simple and clear.

The aim of this paper is to investigate the amenability modulo an ideal of Banach algebras with emphasis on applications to homological algebras. In doing so, we show that amenability modulo an ideal of A^** implies amenability modulo an ideal of A. Finally, for a large class of semigroups, we prove that l¹(S)^** is amenable modulo Iσ^** if and only if an appropriate group homomorphic image of S is finite where Iσ is the closed ideal induced by the least group congruence σ.

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals.

The different cell subsets of the immune system express vitamin D receptor (VDR). Through VDR, vitamin D exerts different functions which influences on immune responses, as previously shown in different preclinical models. Based on this background, retrospective studies have explored the impact of vitamin D levels on the outcome of patients undergoing allogeneic hematopoietic stem cell transplantation, showing that vitamin D deficiency is related to an increased risk of complications, especially graft-versus-host disease. These results have been confirmed in a prospective cohorts trial, although further studies are required to confirm this data. In addition, the role of vitamin D on the treatment of hematologic malignancies has also been explored. Considering this dual effect both on the immune system as well as on tumor cells in patients with hematologic malignancies, vitamin D might be useful in this setting both to decrease graft-versus-host disease and relapse rates.

Superoxide, a form of reactive oxygen species (ROS), is catabolized by superoxide dismutase (SOD) and contributes to carcinogenesis via the oxidative damage it inflicts on cells. The aim of this research was to analyze the potential vitamin D-mediated regulation of the antioxidative “SOD1-to-SOD2 switch” within the human MG-63 osteosarcoma model. For this study; real-time PCR analysis was performed using MG-63 cells exposed to metabolically active 1,25(OH)₂D₃. Frist; a sustained statistically significant >2-fold suppression of proliferating cell nuclear antigen (PCNA) transcripts was observed after 10nM but not at 100nM of 1,25(OH)₂D₃ treatment; suggesting a cytostatic effect. In order to assess regulators of mitochondrial oxidative phosphorylation; gene expression of COX2 and COX4l1 of the mitochondrial complex IV and antioxidative enzymes (SOD1; SOD2 and Catalase (CAT)) were monitored. For COX2 and COX4l1; no changes in gene expression were observed. However; a concomitant decrease in CAT and SOD1 mRNA; and increase in SOD2 mRNA after 24 hours of 10nM 1,25(OH)₂D₃ treatment were observed. A ~8-fold increase in SOD2 mRNA was apparent after 48 hours. The significant increase in SOD2 activity in the presence of vitamin D indicates an antioxidant potential and sensitization of vitamin D during osteosarcoma transformation and mitochondrial detoxification over time.

Hashimoto's thyroiditis (HT) is essentially featured by self-tissue destruction by means of the adaptive immune responses that evade immune regulation. Vitamin D carries out an immunomodulatory role that appears to promote immune tolerance. The aim of this study is to elaborate a narrative review about the relationship between vitamin D status and HT and the role of vitamin D supplementation to reduce HT risk by modulating the immune system. There is an extensive literature confirming that vitamin D levels are significantly lower in HT patients compared to healthy people. On the other hand, after the supplementation with cholecalciferol in patients with HT and vitamin D deficiency, thyroid autoantibody titer decreased significantly, However, there are no conclusive results on the effect of vitamin D supplementation on the thyroid function. The confirmation of the beneficial effects of vitamin D in the prevention and treatment of autoimmune thyroid diseases require additional randomized, double-blind, placebo-controlled trials with longer follow-up.

Vitamin D plays an important role in maintaining healthy mineralized skeleton. It is also consid-ered an immunomodulatory agent that regulate the innate and adaptive immune systems. Multi-ple observational studies have demonstrated the association between low level of serum 25-hydroxyvitamin D [25(OH)D] and presence and severity of several rheumatic diseases, such as rheumatoid arthritis (RA), systemic lupus erythematosus (SLE), spondyloarthropathies and oste-oarthritis (OA). Nevertheless, the specific benefits of vitamin D supplement for treatment and prevention of rheumatic diseases are less accepted as the results from randomized clinical trials are inconsistent, although some conceivable benefits of vitamin D for improvement of disease ac-tivity of RA, SLE and OA have been demonstrated in meta-analyses. It is also possible that some individuals might benefit from vitamin D differently from others since inter-individual difference in responsiveness to vitamin D supplementation has been observed in genomic studies. Although the optimal level of serum 25(OH)D is still debatable, it is advisable it is advisable that patients with rheumatic diseases should maintain serum 25(OH)D level at least 30 ng/mL (75 nmol/L) to prevent osteomalacia, secondary osteoporosis and fracture, and possibly 40 – 60 ng/mL (100 – 150 nmol/L) to achieve maximal benefit from vitamin D for immune health and overall health.

This paper considers the Hermitian solutions of a new system of commutative quaternion matrix equations, we establish both necessary and sufficient conditions for the existence of solutions. Furthermore, we derive an explicit general expression when it is solvable. To illustrate our main findings, we present two numerical algorithms and examples in this paper.

Iyer Markoulakis Helmholtz Hamiltonian mechanics formalisms mathematically modeled physics with vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields. Here, Helmholtz metrics have been gaged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields out of the mechanical fields from Helmholtz Hamiltonian mechanics. This ansatz general gaging helps to properly isolate field effects – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gage metrics, having the power to analyze dark energy superluminal phase, dark matter luminal phase, and light matter subluminal phase. Interpreting particle physics gage matrix pointing to Dirac seas electrons, monopoles with positrons, electron-positron annihilation leading to energy production, relativistic energy generating matter, and both monopoles – vacuum and compressed out of vortex Helmholtz decomposition fields have been interpolated. Quantum ASTROPHYSICS gage metrix posits superluminal profile of signals velocity generating electron-positron chain like “curdling” action that is consistent with physics literature reporting nature electron photon observed oscillatory fields configurations. This helps proposing creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon. These aspects will explain receding or fast expanding universe with dark matter in terms of flavor metrics versus gage associating metrics flavor. Additional interpretations of virtual gravitational dipoles that have gravitational charge of opposite signs, reported per physics literature at Planck dimensions, that may originate at the center of supermassive blackhole. On the other hands, vacuum monopoles occur probably at infinity with cosmos extent.

The calculation of power flow in power systems with the presence of harmonics has been properly studied in the scientific literature. However, power flow calculation considering interharmonic components is still an open question. Traditional methods based on the IEEE1459 standard have proven to be valid and accurate only for linear and sinusoidal systems, but have been criticized for non-linear and non-sinusoidal systems because they are not able to explain correctly the current and voltage interactions beyond the active power. This paper proposes the use of a novel mathematical framework called geometric algebra (GA) to study the power flow considering the interaction of current and voltage harmonics and interharmonics. The use of GA enables the precise determination of the direction and magnitude of the total and single active power flow for each component, as well as other power elements related to the non-active power due to cross interaction. Moreover, this paper makes a novel contribution to the definition of interharmonics in geometric algebra space that has not been done before. To test the validity of the method, both linear and non-linear circuits are proposed and solved by applying voltages and currents with harmonic and interharmonic components. The results obtained show that power flow can be analyzed under the prism of the principle of energy conservation (PoCoE) in a way that allows a better understanding of the power spectrum due to the interaction of harmonics and interharmonics of voltage and current.

A method of solution to solve the compressible unsteady 3D Navier-Stokes Equations in cylindrical co-ordinates coupled to the continuity equation in cylindrical coordinates is presented in terms of an additive solution of the three principle directions in the radial, azimuthal and z directions of flow. A dimensionless parameter is introduced whereby in the large limit case a method of solution is sought for in the boundary layer of the tube. A reduction to a single partial differential equation is possible and integral calculus methods are applied for the case of a body force directed to the centre of the tube to obtain an integral form of the Hunter-Saxton equation. Also an extension for a more general body force is shown where in addition there is a rotational force applied.

Background and Objectives: Previous studies revealed anti-angiogenic, antiproliferative and anti-inflammatory effects of Vitamin D on cancer cells. Although this body of evidence supported the correlation of high Vitamin D levels with reduced incidence rates for various malignancies, contradictory results were reported regarding non-melanoma skin cancer (NMSC). Aim of this overview was to summarize the available evidence from the existing pool of systematic reviews and meta-analyses, focusing on Vitamin D serum status, dietary intake, and Vitamin D receptor (VDR) polymorphisms in correlation to NMSC incidence. Materials and Methods: A literature search in electronic databases was conducted from inception to January 2023. Inclusion criteria were systematic reviews and meta-analyses published in peer-reviewed journals, evaluating Vitamin D serum levels, dietary and/or supplementary intake, or VDR gene polymorphisms, and reporting data on NMSC. Results: A total of 10 studies were included in the data analysis models. A positive association between Vitamin D serum levels and NMSC is highlighted. However, dietary/supplementation of Vitamin D doesn’t exhibit a likewise strong linkage to NMSC. Despite the contradictory findings, VDR polymorphisms may play a crucial role in the intricate NMSC pathogenesis. Conclusions: This umbrella review showed that high Vitamin D levels are associated with increased NMSC incidence, potentially due to its direct correlation with increased sun exposure. Further research on VDR polymorphisms is suggested to explore their true effect size on NMSC risk.

Vitamin D is a nutrient with anti-inflammatory properties whose role is currently being evaluated in COVID-19. Although studies are conflicting, they seem to suggest a role for vitamin D in reducing disease susceptibility but not in improving clinical outcome. In order to understand why vitamin D does not seem to have much effect on decreasing disease severity, it is essential to appreciate pulmonary vitamin D metabolism. To reach the pulmonary compartment, vascular endothelial cells would need to take up vitamin D from the blood stream, but they lack vitamin D receptor (VDR) and the activating enzyme CYP27B1. Endothelialitis – an important disease manifestation of COVID-19 – is therefore not expected to be directly affected by vitamin D. Bronchial epithelial cells are usually among the first to be infected with SARS-CoV-2. They do express both VDR and CYP27B1, but circulating vitamin D may not reach bronchial epithelial cells without transportation from the blood stream through the blood vessel wall. Inhalation therapy with vitamin D has therefore been suggested as an alternative for oral administration to bypass endothelial cells and efficaciously target bronchial epithelium. In conclusion, based on the principles of pulmonary vitamin D metabolism, it is not expected that vitamin D administration has a significant effect on COVID-19 severity. Vitamin D is more likely to reduce SARS-CoV-2 susceptibility, but reaching the airways with oral supplementation will be difficult and vitamin D inhalation therapy should be considered.

Vitamin D has previously been quantified in some plants and algae, particularly in leaves of the Solanaceae family. We measured the vitamin D content of Australian native food plants and Australian-grown edible seaweed. Using liquid chromatography with triple quadrupole mass spectrometry, 13 samples (including leaf, fruit and seed) were analysed in duplicate for vitamin D₂, vitamin D₃, 25-hydroxyvitamin D₂ and 25-hydroxyvitamin D₃. Five samples contained vitamin D₂: raw wattleseed (Acacia victoriae) (0.03 µg/100 g dry weight (DW)); fresh and dried lemon myrtle (Backhousia citriodora) leaves (0.03 and 0.24 µg/100 g DW, respectively); dried leaves and berries of Tasmanian mountain pepper (Tasmannia lanceolata) (0.67 and 0.05 µg/100 g DW, respectively). Fresh kombu (Lessonia corrugata) contained vitamin D₃ (0.01 µg/100 g DW). Detected amounts were low; however, it is possible that exposure to ultraviolet radiation may increase the vitamin D content of plants and algae if vitamin D precursors are present.

The aim of this work is to compare two softwares (MAUD and TOPAS) based on the Rietveld algorithm and to test the concept of tolerance factor using the dissolution at high temperature of yttrium into BaTiO₃. In general, both softwares give up different values of the crystalline parameters however the trends are similar in most cases but the analysis of the strain and crystallite size in the BaTiO₃ crystals suggests that, in this particular case, MAUD offered results more consistent with the expected behavior. Using the crystalline parameters calculated by Rietveld, the tolerance factor values were obtained and these data suggest even better stability in the crystalline structure than that expected using theoretical parameters. Tolerance factor concept also indicates that Ti⁴⁺ should be preferred.

Calorie restriction (CR) has been shown to prolong the lifespan of humans, but enforcing long-term CR is difficult. Therefore, a compound that reproduces the effect of CR without CR is needed. In this review, we summarize the current knowledge on compounds with CR mimetic (CRM) effects. More than 10 compounds have been listed as CRMs, some of which are conventionally categorized as upstream-type CRMs showing glycolytic inhibition while the others are categorized as downstream-type CRMs that regulate or genetically modulate intracellular signaling proteins. Among these, we focus on upstream-type CRMs and propose their classification as compounds with energy metabolism inhibition effects, particularly glucose metabolism modulation effects. The upstream-type CRMs reviewed include chitosan, acarbose, sodium-glucose cotransporter 2 inhibitors, and hexose analogs such as 2-deoxy-D-glucose, D-glucosamine, and D-allulose, which show anti-aging and longevity effects. Finally, we discuss the molecular definition of upstream-type CRMs.

A recent systematic review for 19 selected articles after searching through to 30 September 2017 showed vitamin D deficiency was associated with ischemic stroke (IS), not hemorrhagic stroke (HS). But a heterogeneity would be introduced with comparing the lowest and highest category of vitamin D. The aim of this article was to conduct an updated meta-analysis (UMA) with searching through to 31 March 2019. An interval collapsing method as information extraction was applied in order to decrease a heterogeneity among studies. Additional articles were selected from cited lists from 19 selected articles using citation discovery tools. Random effect model was applied if I-squared value was over 50%. A funnel plot and Egger’s test were used to detect a publication bias. After 5 new studies were added, the summary RRs [and their 95% confidence intervals] (I-squared value) were 1.52 [1.33–1.74] (0.0%) in IS, and 2.44 [1.34–4.46] (69.7%) in HS. This UMA supported the hypothesis that serum vitamin D deficiency was associated with an increased risk of HS as well as IS. Diverse public health programs against vitamin D deficiency status would be needed for higher risk group, especially elderly people.

Upland cotton is sensitive to 2,4-dichlorophenoxyacetic acid (2,4-D), and the identification of potentially 2,4-D tolerant cotton chromosome substitution (CS) lines and understanding tolerance mechanisms provide a significant step into the development and genetic improvement of upland cotton to reduce yield loss caused by 2,4-D herbicide effects including the drifts. Experiments were conducted to understand the possible mechanism of herbicide tolerance in CS-T04-15, CS-T07, and CS-B15sh, 2,4-D herbicide-tolerant cotton CS lines compared with TM-1, the 2,4-D herbicide susceptible recurrent parent of the CS line as control, using [14C]2,4-D. Percent absorption rate and translocation patterns of the 14C-labeled herbicide application at 5.17 kBq at 6 to 48 hours after treatment (HAT) were determined. The tolerant cotton CS lines showed 15-19% [14C]2,4-D uptake while TM-1 exhibited a reduced uptake of only 1.4% [14C]2,4-D at 24 HAT. Distribution of the absorbed [14C]2,4-D showed that 2-5% was translocated outside the treated leaf. In TM-1, 77% of the herbicide was translocated above and below the treated leaf, contrasting with the reduced translocation of 14C-labeled herbicide observed in the tolerant CS lines. Interestingly, CS-T04-15 showed a restricted movement of 14C below the treated leaf at 6 to 48 HAT, suggesting a novel mechanism of herbicide tolerance. This finding is the first report on upland cotton demonstrating a complex differential uptake and translocation associated with herbicide tolerance for [14C]2,4-D in cotton CS lines.

Backgroundː Previous studies have shown that both serum creatinine and D-dimer levels were associated with atherosclerotic coronary artery disease (CAD). We aimed to determine whether DCR is associated with coronary Gensini score in patients with ST-elevation myocardial infarction (STEMI). Methodsː 337 STEMI patients with complete D-dimer and creatinine and other necessary information were included in the analysis. According to the values of the DCR, patients were divided into the lower DCR group (DCR ≤ 1.42, n = 173) and the higher DCR group (DFR > 1.42, n = 174), and the differences between the two groups were compared. Multivariate linear and multivariate logistic regression analyses were performed to determine independent predictors of Gensini score. Resultsː High DCR group had higher Gensini score compared with low DCR group (P < 0.05). DCR was positively correlated with Gensini score (r=0.493, P < 0.001). Multiple linear regression analysis showed that Previous MI (r=11.312, P=0.035) and DCR (r=5.129, P<0.001) were independent risk factors associated with Gensini score. Multivariate logistic regression analysis showed that, compared to the group 1, DCR is independent risk factor for Group 2, Group 3, Group 4 (P <0.001). DCR is positively correlated with coronary Gensini score in STEMI patients and can be used as an independent predictor of higher Gensini score. Conclusionsː As a new and useful clinical marker, DCR is positively correlated with coronary Gensini score in STEMI patients and can be used as an independent predictor of higher Gensini score.

The goal of the paper is to clarify the observed irrationality of decision making in conflict situations considered as one-step games of two players. To solve such situations, we consider the asymmetry in the relation of the players to their own rewards and the rewards of the opponents. Formalization of the decision-making process is based on recently developed non-commutative operators of multivalued logic algebra. The suggested method is applied to solve the well-known Prisoners’ dilemma game and the other situations of conflict, where it results in the expected strategies.

The switching game Lights Out and its variants were studied extensively as recreational mathematics problems. The game board of the ordinary Lights Out is a rectangular grid of lights, where each light is either on or off. By clicking a light, the clicked light and its adjacent rectilinear neighbors are toggled. Given an arbitrary initial configuration of lights, the final mission is to “solve” this game by switching off all the lights. Most studies on Lights Out and its variants focused on the solvability of given games or the number of solvable games, but when the game is viewed in a coding-theoretical perspective, more interesting questions with special meanings in coding theory will naturally pop up, such as finding the minimal number of lit lights among all solvable games except the solved game, or finding the minimal number of lit lights that the player can achieve from a given unsolvable game, etc. However, these problems are usually hard to be solved in general in terms of algorithmic complexity. This study considers a natural extension of the Lights Out game, which enlarges the toggle pattern in a way that all the lights in the same row and those in the same column of the clicked light are toggled. This variant of Lights Out is a two-state version of a switching game called Alien Tiles. In this paper, we investigate the properties of the two-state Alien Tiles, and discuss several coding-theoretical problems about this game. Then, we apply this game as an error correction code and investigate its optimality. We also give a brief overview on algorithmic complexity and coding theory for readers who are not familiar with these topics. The purpose of this paper is to propose ways of playing switching games in a think-outside-the-box manner, which benefit the recreational mathematics community.

In this paper, we generalize Fibonacci quaternion, octonion, sedenion, trigintaduonion, etc. and define Horadam 2^{k}-ions and investigate their properties. Each Horadam (such as Fibonacci, Lucas, Pell) quaternions, octonions and sedenions are Horadam 2^{k}-ions. We also present connection to some earlier works.

The Heisenberg Lie algebra (HA) plays an important role in mathematics with Fourier transforms, as well as for the foundations of quantum theory where it expresses the operators of space-time, X, and their commutation rules with the momentum operators, D, that execute infinitesimal translations in X. Yet it is known that space-time is curved and thus the D operators must interfere thus giving “structure constants” that vary with location which suggests a mathematical generalization of the concept of a Lie algebra to allow for “structure constants” that are functions of X. We here investigate the mathematics of such a “generalized Heisenberg algebra” (GHA) which has “structure constants” that are functions of X and thus are in the enveloping algebra rather than constants. As expected, the Jacobi identity no longer holds globally but only in small regions of space-time where the [D, X] commutator can be considered locally constant and thus where one has a true Lie algebra. We show that one is able to reframe Riemannian geometry in this GHA. As an example, it is then shown that one can express the Einstein equations of general relativity as commutation rules. If one requires that the GHA commutator reduces to the HA of quantum theory in the limit of no curvature, then there are observable effects for quantum theory in this curved space time.

Non-linear loads in circuits cause the appearance of harmonic disturbances both in voltage and current. In order to minimize the effects of these disturbances and, therefore, to control over the flow of electricity between the source and the load, they are often used passive or active filters. Nevertheless, determining the type of filter and the characteristics of their elements is not a trivial task. In fact, the development of algorithms for calculating the parameters of filters is still an open question. This paper analyzes the use of genetic algorithms to maximize the power factor compensation in non-sinusoidal circuits using passive filters, while concepts of geometric algebra theory are used to represent the flow of power in the circuits. According to the results obtained in different case studies, it can be concluded that the genetic algorithm obtain high quality solutions that could be generalized to similar problems of any dimension.

Age-related declines in vitamin D receptor (VDR) expression have been implicated in the onset of sarcopenia. The increased expression of VDR in muscle is known to increase muscle mass, whereas VDR knockout in the muscle decreases muscle mass in rats. Similar to VDR, the age-related decline in protein deacetylase sirtuin (SIRT) expression is linked to the development of sarcopenia and age-related muscle dysfunction. This study aimed to investigate whether the VDR agonist 1,25-dihydroxyvitamin D3 (1,25VD3) exerts beneficial effects on muscles through interactions with sirtuins and, if so, the underlying molecular mechanisms. 1,25VD3 treatment increases the expression of VDR, SIRT1, and SIRT3 in C2C12 myotubes. Additionally, it stimulates the differentiation of C2C12 myoblasts into myotubes. Furthermore, 1,25VD3 significantly enhanced the expression of key myogenic markers, including myosin heavy chain (MyHC) proteins (MyHC I and II), MyoD, and MyoG, and increased the phosphorylation of AMPK and AKT. Conversely, VDR knockdown in myoblasts induces myotube atrophy by downregulating SIRT1 and SIRT3 expression. Furthermore, 1,25VD3 ameliorated muscle atrophy and apoptosis induced by IFN-γ/TNF-α co-treatment to C2C12 myotube. Moreover, 1,25VD3 downregulated the increased expression of muscle atrophy-associated proteins, including FoxO3a, MAFbx, and MuRF1 in IFN-γ/TNF-α induced atrophy model. Importantly, IFN-γ/TNF-α significantly reduced the mtDNA copy number in C2C12 myotube, whereas the presence of 1,25VD3 effectively prevented this decrease. These results indirectly suggest that 1,25VD3 has the potential to develop as a therapeutic or preventive agent for age-mediated muscle atrophy by enhancing the VDR/SIRT1/SIRT3 axis and inhibiting the FoxO3-mediated atrophy pathway.

Rapid industrialization, urbanization, and population explosion in sub-Saharan Africa escalate environmental Lead levels with subsequent elevation of blood Lead levels in children. Nutrition status, age, and genetics govern one’s susceptibility to Lead toxicity. This study expounded this susceptibility by relating blood Lead levels, d-aminolevulinic acid dehydratase enzyme activity (ALAD), and genetic variations of proteins that code for ALAD enzyme in urban children of Uganda. Spectrophotometric analysis for blood Lead (BL), hemoglobin levels, and determination d-levels aminolevulinic acid dehydratase enzyme activity of the blood samples from 198 children were performed prior to a polymerase chain reaction and restriction fragment length digestion for ALAD polymorphism was done. Up to 99.5% of samples coded for the ALAD1 allele whereas 0.05% coded for ALAD2. Genotypes ALAD2-2 members had elevated BLL (mean 14.1 µg/dL) and reduced ALAD enzyme activity compared to others. This, therefore, implies that the majority of children hoard BL which may affect them later in life.

Vitamin D has important anti-inflammatory, anti-microbial properties and plays a central role in host immune response. Due to the crucial role of the kidneys in the metabolism of vitamin D, patients with chronic kidney disease (CKD), are prone to vitamin D deficiency. The resultant reduction in the production of calcitriol, the activated form of vitamin D in patients with CKD is responsible for exacerbating the existing renal impairment and periodontal inflammation. Recent evidence suggests a bidirectional, causal relationship between periodontitis and renal functional status. Both conditions have shared pathophysiologic mechanisms including oxidative stress, increases in the systemic inflammatory burden and impaired host response. This review explores the association between vitamin D, CKD and periodontitis. The review summarises the current evidence base for the classical and non-classical vitamin D metabolic pathways, the biological mechanisms linking vitamin D deficiency, CKD and periodontitis, as well as the bidirectional relationship between the two chronic inflammatory conditions. Finally, the paper explores the impact of vitamin D deficiency on CKD, periodontitis, and related co-morbidities.

D-Serine, a co-agonist of NMDA receptors has sparked a contentious debate within the scientific community regarding its status as a gliotransmitter or a neurotransmitter. This comprehensive review delves into the heart of this debate, offering a meticulous analysis of the existing evidence from various research methodologies. Immunostaining studies and cell-selective mutations provide compelling support for D-serine's neuronal origin, bolstering the serine shuttle model. In contrast, the gliotransmission hypothesis, proposing astrocytic synthesis and release, faces critical scrutiny as inconsistencies in supporting data emerge. In vivo microdialysis experiments unveil a neuronal contribution to D-serine release and its profound impact on synaptic plasticity, further strengthening the case for neuronal dominance. Counterarguments in favor of astrocytic D-serine release are systematically dissected, revealing inherent limitations and ambiguities. Collectively, the evidence corroborates D-serine's neuronal source and discounts the astrocytic hypothesis. This review underscores the need for scientific rigor when evaluating contentious topics and affirms the simplicity of the neuronal explanation, aligning D-serine with the serine shuttle model, thus advancing our comprehension of its pivotal role in synaptic function and cognitive processes. As the debate continues to evolve, this exploration encourages ongoing research to unravel the intricate mechanisms governing D-serine neurotransmission.

Cellulose nanocrystals (CNCs) are a kind of nano-inclusions that have experienced tremendous expansion in the material industry due to their outstanding mechanical qualities, sizable surface area, and capacity for functional tuning. Due to their vast potential, however, present practises fall short of fully using them. For example, employing CNCs in various matrices with various surface chemistries can be challenging; this problem tends to get worse if the focus is furthered on bio-based applications. This paper reviews the use of CNCs as fillers in natural and man-made polymers; we have explored in depth the production, characterisation, and of CNCs from various sources and their inclusion into various matrices. Surface alterations and the introduction of CNCs in biodegradable polymer can have a significant impact on several industrial behemoths such as tissue engineering and biomedical applications; therefore, pursue of current manuscript is extremely warranted. Throughout the manuscript various assembly techniques that involves alteration and adjustment of polymer network in building up a hydrogel with higher fracture energy and mechanical properties are also included. From rheological perspective the hydrogel processing is also discussed with some models routinely used in the literature to describe these hydrogels. Finally, bio-based hydrogels mechanically reinforced with CNCs such as Xanthan Gum, Alginate, protein, and polysaccharides were discussed.

Background: A Few preclinical studies have shown that Knee osteoarthritis (KOA) is linked to gut microbiome dysbiosis and chronic inflammation. This pilot study was designed to look at the gut microbiome composition in KOA patients and normal individuals with or without vitamin D deficiency (VDD, serum vitamin D <30 ng/ml). Methods: This pilot study was conducted prospectively in 24 participants. The faecal samples of all the participants were taken for DNA extraction. The V3-V4 region of 16s rRNA was amplified and the library was prepared and sequenced on the Illumina Miseq platform. Results: The mean (±SD) age was 45.5 (±10.2) years with no defined co-morbidities. Of 447 total Operational Taxonomic Units (OTUs), a differential abundance of 16 nominally significant OTUs between the groups were observed. Linear discriminate analysis (LEfSe) revealed a significant difference in bacteria among the study groups. Pseudobutyrivibrio and Odoribacter were specific for VDD while Parabacteroides, Butyricimonas, and Gordonibacter were abundant in the KOA_VDD group and Peptococcus, Intestimonas, Delftia, and Oribacterium were abundant in the KOA group. About 80% of bacterial species were common among different groups and hence labeled as core bacterial species. However, the core microbiome of KOA and VDD groups were not seen in the KOA_VDD group, suggesting that these bacterial groups were affected by the interaction of the KOA and VDD factors. Conclusion: Parabacteroides, Butyricimonas, Pseudobutyrivibrio, Odoribacter, and Gordonibacter are the predominant bacteria in vitamin D deficient patients with or without KOA. Together these results indicate an association between the gut microbiome, vitamin D, and knee osteoarthritis.

Coronavirus disease (COVID-19) is an infectious disease caused by a new virus which causes respiratory illness. Older adults and people who have previous chronic medical conditions are at higher risk for more serious complications from COVID-19.Hypovitaminosis D is attributed to the increased risk of lung injury and acute respiratory distress syndrome (ARDS) as well as diabetes, Cardiovascular event and associated comorbidities, which are the main causes of severe clinical problem in COVID-19 patients. Considering the protective role of vitamin D through modulating the innate and adaptive immune system as well as inhibition of Renin Angiotensin System (RAS), vitamin D supplementation might boost the immune system of COVID-19 patients and reduce severity of the disease in vitamin D deficient individuals.

The InSAR technique measures the displacement of an indicator using SAR image interference. The technique of interfering two SAR images among InSAR techniques is called Differential InSAR (D-InSAR). In the process of D-InSAR, the filtering technique is used in the Unwrapped Mask, usually using the GoldStein method. However, since the Goldstein method removes the noise on the path, it is difficult to derive the displacement value in the agricultural area where the relative coherence is low. In Korea, more than 50% of the whole country consists of mountainous regions and agricultural regions, so it is difficult to use the Goldstein technique polysynthetically. In this study, we set the test-bed for the urban area and the agricultural area based on Coherence, and introduce Goldstein and Boxcar Filter, one of the Goldstein and LSM techniques. Through this process, we want to draw the conclusion which is displacement values ​​in the agricultural area.

Recent studies have demonstrated a relationship between poor vitamin D status and respiratory infections and diarrhea among young children. Acute lower respiratory infections (ALRI) and diarrhea are among the two most important causes of death in under-5 children. In this analysis, we examine the extent to which vitamin-D deficiency (<10 ng/ml) predicts these outcomes using data from a randomized controlled trial (RCT) of daily folic acid and/ or vitamin B12 supplementation for six months in 6 to 30 months old children conducted in Delhi, India. Of the 960 subjects who had vitamin-D concentrations measured, 331(34.5%) were vitamin-D deficient. We found, after controlling for relevant potential confounders (age, sex, breastfeeding status, wasting, stunting, underweight, anemia status at base line and season), the risk of ALRI was significantly higher among vitamin-D deficient (OR 1.26; 95% CI: 1.03 to 1.55) compared to vitamin-D-replete children in the six months follow-up period. Vitamin-D status was not significantly associated with episodes of diarrhea and clinical pneumonia. The extent of causal relationship of vitamin-D status and ALRI needs to be explored in further studies.

(1) Background: Obesity and its comorbidities can cause burdens and limitations. Bariatric surgery (BS) is indicated as a safe procedure to reduce body mass and improve present comorbidities. Yet, several complications were reported, like vitamin D [25(OH)D] deficiency. We evaluated if 25(OH)D serum levels relate to clinical characteristics, symptoms, or habits in women after their BS and whether the vitamin D receptor (VDR) gene's TaqI and FokI polymorphisms affected 25(OH)D levels and the total body bone mineral density (TBBMD). (2) Methods: This cohort cross-sectional comparative analytical prospective study consisted of 27 women, 61.6 ± 5.0 years, submitted to BS one year prior at a public reference hospital, DF-Brazil. All participants were asked to follow the physical and dietary activity recommendations and received vitamin D3 supplements. Their anthropometric, biochemical, and immunological measurements and blood samples were obtained. (3) Results: 73.3% of participants had low 25(OH)D levels, and their levels correlated positively with TBBMD and negatively with systolic pressure. VDR TaqI did not affect 25(OH)D levels, whereas VDR FokI's allele f presence correlated to a median rise in 25(OH)D levels. Neither polymorphism correlated to TBBMD. (4) Conclusions: 25(OH)D levels were positively correlated with TBBMD, negatively with systolic blood pressure, and were higher in those with the VDR FokI allele f.

Chronic oxidative stress in long-distance runners adversely affects conditioning. Therefore, it is important to objectively assess and monitor oxidative stress but measuring oxidative stress can be invasive or require skill to measure. Therefore, this study aimed to verify whether skin autofluorescence (SAF), a noninvasive, rapid, and easily calculable metric for calculating advanced glycation end products (AGEs), is useful as an oxidative stress biomarker. The subjects were 50 young Japanese male long-distance runners (aged 20.2 ± 1.2 years); 35 average male university students (aged 19.8 ± 1.1 years) served as controls. The interactions and relationships between SAF and plasma pentosidine and oxidative stress markers (reactive oxygen metabolite-derived compounds [d-ROMs], biological antioxidant potential [BAP], and the BAP/d-ROMs ratio) in runners were examined, and SAF in the runners and controls was compared. The results suggest that plasma pentosidine in runners is associated with oxidative stress markers and that plasma pentosidine can assess oxidative stress. However, SAF was not validated as an oxidative stress marker because it was not associated with oxidative stress marker. In future, clarifying the factors affecting SAF may clarify the relationship between SAF, plasma pentosidine, and oxidative stress markers.

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra $J_3(\mathbb O)$ [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group $F_4$. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the groups $F_4$ and $E_6$ could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a $U(1)$ number operator, identified with $U(1)_{em}$. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for quarks and charged leptons. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an $F_4$ and $E_6$ symmetry. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value $1/137.04006$. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

The new barrier mode in Apache Spark allows embedding distributed deep learning training as a Spark stage to simplify the distributed training workflow. In Spark, a task in a stage doesn’t depend on any other tasks in the same stage, and hence it can be scheduled independently. However, several algorithms require more sophisticated inter-task communications, similar to the MPI paradigm. By combining distributed message passing (using asynchronous network IO), OpenJDK’s new auto-vectorization and Spark’s barrier execution mode, we can add non-map/reduce based algorithms, such as Cannon’s distributed matrix multiplication to Spark. We document an efficient distributed matrix multiplication using Cannon’s algorithm, which improves significantly on the performance of the existing MLlib implementation. Used within a barrier task, the algorithm described herein results in an up to 24% performance increase on a 10,000x10,000 square matrix with a significantly lower memory footprint. Applications of efficient matrix multiplication include, among others, accelerating the training and implementation of deep convolutional neural network based workloads, and thus such efficient algorithms can play a ground-breaking role in faster, more efficient execution of even the most complicated machine learning tasks

We study almost hypercomplex structure with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. All the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on one parameter are investigated. There are studied some geometrical characteristics of the respective almost hypercomplex manifolds with Hermitian-Norden metrics.

The Process Algebra model has been shown to provide an alternative mathematical framework for non-relativistic quantum mechanics (NRQM). It reproduces the wave functions of non-relativistic quantum mechanics to a high degree of accuracy. It posits a fundamental level of finite, discrete events upon which the usual entities of NRQM supervene. It has been suggested that the Process Algebra model provides a true completion of NRQM, free of divergences and paradoxes, with causally local information propagation, contextuality and realism. Arguments in support of these claims have been mathematical. Missing has been an ontology of this fundamental level from which the formalism naturally emerges. In this paper it is argued that information and information flow provides this ontology. Higher level constructs such as energy, momentum, mass, spacetime, are all emergent from this fundamental level.

The QCD Lagrangian is based on quark and gluonic fields -- not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a representation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. % The pion $q \bar q$ eigenstate has zero mass for $m_q=0.$ % % A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale $\kappa$ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also predicts the form of the nonperturbative QCD running coupling: $\alpha_s(Q^2) \propto e^{-{Q^2/4 \kappa^2}}$, in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. % The combination of conformal symmetry, light-front dynamics, its holographic mapping to AdS$_5$ space, and the dAFF procedure thus provide new insights, not only into the physics underlying color confinement, but also the nonperturbative QCD coupling and the QCD mass scale.

With the advent of COVID19, the attitude of health authorities around the world, led mainly by the West, demanded a level of proof as evidence for cheap, non-patented remedies while promoting expensive, patented, and untested remedies by using emergency use authorization and special provisions afforded to the status of a pandemic emergency. Western science has neither a tested nor a valid historical basis of a logical system that informs to authenticate scientific practices. Here we use a logical heuristic derived from ancient Buddhist logic, which is consistent with the conduct of modern science. We applied the heuristic to show that enough evidence was available for using cost-effective early therapies such as vitamin D supplementation as a public health measure during the first half of 2020. Strong supporting evidence has since accumulated. Apart from political and financial decisions incompatible with science and other conflicts of interest, a critical barrier to evaluating and approving early therapies appears to be the fallacy that the randomized controlled trial (RCT) is the superior proof method in medical hypotheses, including those for nutrients. Logically, no reason exists why properly designed retrospective, ecological, and naturalistic studies with adequate sample sizes and applied appropriate statistical methods would not be as valid as RCTs, especially when elucidating a causative factor instead of treatment. That assertion is particularly true for nutrient deficiencies, interventions, and other cost-effective therapies. Leading health authorities’ failure or refusal to consider other study types (because of either poor logic or vested interest) probably contributed to the spread of misinformation, symptomatic disease, complications, and deaths from COVID19. Partial immunity derived from vaccines and the later development of more contagious variants—and thus a sense of acceptance that SARS-CoV-2 had progressed from a pandemic to an endemic—shows the hollowness of the initial promotions and mandates of vaccines as a cure. Adequate knowledge was available in 2020 to advise that SARS-CoV-2 will continue to mutate, with variants emerging a few times per year, making the vaccine less effective. Emerging evidence confirms that natural immunity better protects against new variants than vaccination against the spike protein. Had vitamin D been adopted as part of the public health measure through a broader supplementation program in 2020 or even today (through sun exposure or as a prophylactic or adjunct therapy early on), the viral spread and symptomatic disease may have been suppressed, with minimal lockdowns and quarantine, and economic harm. The pandemic could have been halted with a significantly reduced need for hospitalization, complications, and deaths, potentially saving millions of lives.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

Motivated from the theory of Hilbert-Schmidt morphisms between Hilbert C*-modules over commutative C*-algebras by Stern and van Suijlekom [J. Funct. Anal., 2021], we introduce the notion of p-absolutely summing morphisms between Hilbert C*-modules over commutative C*-algebras. We show that an adjointable morphism between Hilbert C*-modules over monotone closed commutative C*-algebra is 2-absolutely summing if and only if it is Hilbert-Schmidt. We formulate version of Pietsch factorization problem for p-absolutely summing morphisms and solve partially.

In this paper, by using the q-integer, we introduce a new generalization of Fibonacci and Lucas sedenions called q-Fibonacci and q-Lucas sedenions. We present some fundamental properties of these type of sedenions such as Binet formulas, exponential generating fuctions, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity.

The present paper discusses a study of a class of Charlier matrix polynomials and its generalized analogue. Certain generating matrix functions, recurrence matrix relations, matrix differential equation, summation formulas and many new results have been discussed for these matrix polynomials. Weisner's group theoretic method is used to obtain matrix generating relations for Charlier matrix polynomials and the details of this method were given in this paper. Finally, we will discuss only briefly the procedure followed.

We explore the class of positive integers n that admit idempotent factorizations n=pq such that lambda(n) divides (p-1)(q-1), where lambda(n) is the Carmichael lambda function. Idempotent factorizations with p and q prime have received the most attention due to their cryptographic advantages, but there are an infinite number of n with idempotent factorizations containing composite p and/or q. Idempotent factorizations are exactly those p and q that generate correctly functioning keys in the RSA 2-prime protocol with n as the modulus. While the resulting p and q have no cryptographic utility and therefore should never be employed in that capacity, idempotent factorizations warrant study in their own right as they live at the intersection of multiple hard problems in computer science and number theory. We present some analytical results here. We also demonstrate the existence of maximally idempotent integers, those n for which all bipartite factorizations are idempotent. We show how to construct them, and present preliminary results on their distribution.

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.

The association between depressive symptomatology and cognitive decline has been examined using the Centre for Epidemiologic Studies-Depression Scale (CES-D), however, concerns have been raised about this self-report measure. Here, we examined how the CES-D total score from the 14- and 10-item versions compared to the 20-item version in predicting progression to cognitive decline from a cognitively unimpaired baseline. Data from 1,054 participants were analysed using ordinal logistic regression, alongside moderator and receiver-operating characteristics curve analyses. All baseline total scores significantly predicted progression to cognitive decline. The 14-item version was better than the 20-item version in predicting consensus diagnosis, as shown by their AICs, while also showing the highest accuracy when discriminating between participants by diagnosis at last visit. We did not find sex to moderate the relationship between CES-D score and cognitive decline. Current findings suggest the 10- and 14-item versions of the CES-D are comparable to the 20-item version, and that the 14-item version may be better at predicting longitudinal consensus diagnosis compared to the 20-item version.

Background/Aim: Rapid onset of facial ptosis can impact physical appearance and compromise the outcomes of facelift procedures. The level of vitamin D has a potential correlation with collagen formation and its deficiency with inflammatory processes that affect the breakdown of hyaluronic acid. This study aims to investigate the potential relationship between accentuated facial ptosis in women and low levels of vitamin D. Furthermore, it aims to explore preventive measures or strategies to slow down facial ptosis and enhance the longevity of facelift results. Materials and Methods: The study was focused on monitoring the vitamin D levels in women and men with advanced facial ptosis and comparing them with a control group. Results: Notably, a direct association between gender and serum vitamin D levels was observed, indicating less sustainable outcomes in women. Conclusion: Women face additional challenges in the aging process due to hormonal shifts after menopause or premenopausal, which are associated with osteoporosis and lower vitamin D levels.

(1) Background: The HIV subtype D is generally associated with a faster decline in CD4+ T cell counts, a higher viral load, and a faster progression to AIDS. However, it is still poorly characterized in Brazil. In this study, we used genomics and epidemiological data to investigate the transmission dynamics of HIV subtype D in the state of Bahia, Northeast Brazil. (2) Methods: to achieve this goal, we obtained four novel HIV-1 subtype D partial pol genome sequences using the Sanger method. To understand the emergence of this novel subtype in the state of Bahia, we used phylodynamic analysis on a dataset comprising 3,704 pol genome sequences downloaded from the Los Alamos database. (3) Results: Our analysis revealed three branching patterns, indicating multiple introductions of the HIV-1 subtype D in Brazil from the late 1980s to the late 2000s and a single introduction event in the state of Bahia. Our data further suggest that these introductions most likely originated from European, Eastern African, Western African and Southern African countries. (4) Conclusion: Understanding the distribution of HIV-1 viral strains and their temporal dynamics is crucial for monitoring the real-time evolution of circulating subtypes and recombinant forms, as well as for designing novel diagnostic and vaccination strategies. We advocate for a shift to active surveillance, to ensure adequate preparedness for future epidemics mediated by emerging viral strains.

It is a well-established fact that inadequate Vitamin D (Vit-D) levels have negative effects on the development and progression of malignant diseases, mainly cancer. The purpose of this paper was to elucidate the effects of Vit-D intake and serum 25-hydroxyvitamin-D (25(OH)D) levels on cancer incidence and mortality, the current evidence in this field, and the biases of this evidence using the meta-meta-analysis method. Meta-analyses focusing on Vit-D intake, serum 25(OH)D levels, and cancer risk/mortality were identified. A structured computer literature search was performed in PubMed/Medline, Web of Science (WoS), and Scopus electronic databases using predetermined keyword combinations. Primary and secondary meta-meta-analyses were carried out, combining odds ratios (ORs), risk ratios (RRs), and hazard ratios (HRs) for outcomes reported in selected meta-analyses. A total of 35 eligible meta-analyses assessing the association between Vit-D and cancer incidence and/or mortality were included in this study. In the pooled analysis, higher Vit-D intake and serum 25(OH)D levels were associated with lower cancer risk (OR = 0.93, 95% CI: 0.90-0.96, p < 0.001; OR = 0.80, 95% CI: 0.72-0.89, p < 0.001, respectively) and cancer-related mortality (RR = 0.89, 95% CI: 0.86-0.93, p < 0.001; RR = 0.67, 95% CI: 0.58-0.78, p < 0.001, respectively). When meta-analyses whose primary reports included only randomized controlled trials were pooled, there was no significant association between Vit-D intake and cancer risk (OR = 0.99, 95% CI: 0.97-1.01, p = 0.320). In subgroup analysis, Vit-D consumption was associated with a significant decrease in colorectal and lung cancer incidence (OR = 0.89, 95% CI: 0.83-0.96, p = 0.002; OR = 0.88, 95% CI: 0.83-0.94, p < 0.001, respectively). Taken together, both Vit-D intake and higher 25(OH)D levels may provide remarkable benefits in terms of cancer incidence and mortality, however, careful evaluation according to cancer types is critically important and recommended.

The paper summarizes the current knowledge about the structure, species, and content differ-ences of β-D-glucans as a storage and functional component, especially of cereal grains. The pa-per also provides comprehensive information on the biosynthesis of this plant cell wall polysac-charide, genetic and non-genetic factors influencing the content variability and indicates the pos-sibilities of breeding modern varieties with a defined content of this metabolite. The final part of the text is also devoted to the influence of significant technological processes applied to cere-als containing β-D-glucans. The chapter discusses the influence of these processes on the content and structure of the polysaccharide and the resulting changes in its physicochemical properties. Part of the discussed issue are the possibilities of effective application of β-D-glucans in different food products.

Brain fog with compromised ability to concentrate has been the most frequent Long Covid (LC) complaint. This is due to an increased transforming growth factor (TGF) β/interferon (IFN)-γ ratio with consequently increased bradykinin (BKN), especially in Caucasian females. Brain and lung blood vessels “leak.” This same ratio is increased in Alzheimer’s disease (AD), but decreased in Parkinson’s disease (PD), because CD4⁺ and CD8⁺ T cells are differentially affected by the invading associated viruses, e.g., SARS CoV2, HIV, Varicella Zoster (VZV) aka Human Herpesvirus 3 (HHV3), HBV, HCV, …. In Covid-19 CD147 receptors on immune cells are critical in generating the increased TGF-β/IFN-γ and those on endothelial cells, platelets, and erythrocytes are critical to the abnormal microvascular blood flow. ACE2 receptors on pneumocytes and enterocytes enable pulmonary and GI entry, initiating gut dysbiosis. Epigenetics, methylation, magnesium, vitamin D, the B vitamins, and antioxidants suggest that these issues can be surmounted. Biochemical, physiologic, and epidemiologic data are analyzed to answer these questions. An LC model is presented and discussed in the context of the most recent research. Suggestions to avoid these and other worrisome concerns are included. Other topics discussed include estrogen, the gut microbiome, type 2 diabetes (T2D), and homocysteine.

This research aims to obtain empirical evidence of the influence of the masculinity of male CEOs on the of research & development, this research seeks to identify the influence of the face of mas-culinity of male CEO’s on the of research & development. The study used a quantitative approach with population and research samples using companies listed on the Indonesia Stock Exchange from 2016 to 2021. The study collected images of faces identified as male CEOs from data from the Indonesia Stock Exchange website and company as utilizing Google searches. The data analysis method in this study used Regression Ordinary Least Square (OLS) with Stata Software. Stata software is one of the regression completion procedures that has a high degree of flexibility in re-search that connects theories, concepts and data that can be done on variables in research. The findings empirically explain that the higher the face value of male CEO masculinity has an impact on reducing research & development costs, and vice versa the lower the face value of male CEO masculinity has an impact on increasing research & development. The practical implications of the research results can help the Indonesian Association of Accountants in developing Financial Accounting Standard No. 19 in Indonesia. The theoretical implications of the research results can explain the Theory of Agency and the Theory of Consistency of Behavior. The policy implications of the results of the study can provide empirical evidence that the higher the facial value of male CEO masculinity has an impact on reducing research & development, while also the lower the face value of male CEO masculinity has an impact on increasing research & development.

Abstract: The genus Acaryochloris is unique among phototrophic organisms due to the dominance of chlorophyll d in its photosynthetic reaction centres and light-harvesting proteins. This allows Acaryochloris to capture light energy for photosynthesis over an extended spectrum of up to ~760 nm in the near infra-red (NIR) spectrum. Acaryochloris sp. has been reported in a variety of ecological niches, ranging from polar to tropical shallow aquatic sites. Here, we report a new Acarychloris strain isolated from an NIR-enriched stratified microbial layer 4-6 mm under the surface of stromatolite mats located in the Hamelin Pool of Shark Bay, Western Australia. Pigment analysis, by traditional spectrometry/fluorometry, flow cytometry and spectral confocal microscopy identify unique patterns in pigment distribution that likely reflect niche adaption. For example, unlike the original A. marina species (type strain MBIC11017), this new strain, Acarychloris LARK001, shows little change in the chlorophyll d/a ratio in response to changes in light wavelength, displays a different Fv/Fm response and lacks detectable levels of phycocyanin. Indeed, 16S rRNA analysis supports the identity of the A. marina LARK001 strain as distinct from the A. marina HICR111A strain first isolated from Heron Island, previously found on the Great Barrier Reef, under coral rubble on the reef flat. Taken together, A. marina LARK001 is a new cyanobacterial strain adapted to the stromatolite matts in Shark Bay.