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.

Kim-Kim ([9]) studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace Transformation and investigate some properties and formulas related to them.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

Radio loud active galactic nuclei are composed of different spatial features, each one characterized by different spectral properties in the radio band. Among them, blazars are the most common class of sources detected at gamma-rays by \fermi, and their radio emission is dominated by the flat spectrum compact core. In this contribution, we explore the connection between emission at high energy revealed by \fermi\ and at radio frequency. Taking as a reference the strong and very highly significant correlation found between gamma rays and cm-$\lambda$ radio emission, we explore different behaviours found as we change the energy range in gamma rays and in radio, therefore changing the physical parameters of the zones involved in the radiation emission. We find that the correlation weakens when we consider (1) gamma rays of energy above 10 GeV (except for high synchrotron peaked blazars) or (2) low frequency radio data taken by the Murchison Widefield Array; on the other hand, the correlation strengthens when we consider mm-$\lambda$ data taken by ALMA.

QSO B0218+357 is a blazar located at a cosmological redshift of 0.944. The source is gravitationally lensed by a spiral galaxy located at the redshift of 0.68. Strong gravitational lensing splits the signals emitted by the source into two components separated by 10-12 days, as observed in radio and gamma-ray bands. In July 2014 a GeV flare was observed by Fermi-LAT, triggering follow-up observations with the MAGIC telescopes at energies above 100 GeV. The expected time delay between the components allowed us to plan broad band MWL observations before, during and after the trailing component of the emission. The MAGIC observations at the expected time of arrival of the trailing component resulted in the first detection of QSO B0218+357 in Very-High-Energy (VHE, >100 GeV) gamma rays. It is both the farthest known VHE object and one of only a few Flat Spectrum Radio Quasars detected in this energy range. We report here the observed multiwavelength spectral and temporal properties of the emission during the 2014 flare.

Present work investigates, in photon energy domains of specific interest for medical imaging, the effect of the escape of X-ray fluorescence from the scintillator materials on the energy resolution of scintillation detector itself. Monolithic as well as pixelated crystals differently sized are considered, in the case of the NaI because it is the gold standard in the field. The volumetric ratio is introduced, as a figure of merit, taking into account, alongside the surface-to-volume ratio, the geometric shape, the elemental composition and also the mean-free-path for the given scintillator and energy. The inter-crystal XRF escape is finally suggested to be considered among the effects producing image blurring in segmented scintillatros due to the spread of events between the primary pixel and the first neighbors ones.

Liver fibrosis is a critical health issue with limited treatment options. This study investigates the potential of PGC-Sec, a secretome derived from PGC-1α-overexpressing adipose-derived stem cells (ASCs), as a novel therapeutic strategy for liver fibrosis. Upon achieving a cellular confluence of 70-80%, ASCs were transfected with pcDNA-PGC-1α. PGC-Sec, obtained through concentration of conditioned media using ultrafiltration units with a 3-kDa cutoff, was assessed through in vitro assays and in vivo mouse models. In vitro, PGC-Sec significantly reduced LX2 human hepatic stellate cell proliferation and mitigated mitochondrial oxidative stress compared to control-secretome (Ctrl-Sec). In an in vivo mouse model, PGC-Sec treatment led to notable reductions in hepatic enzyme activity, serum pro-inflammatory cytokine concentrations, and fibrosis-related marker expression. Histological analysis demonstrated improved liver histology and reduced fibrosis severity in PGC-Sec-treated mice. Immunohistochemical staining confirmed enhanced expression of PGC-1α, OPA1 (a mitochondrial function marker), and PPARα (an anti-fibrogenic marker) in the PGC-Sec-treated group, along with reduced Collagen 1A expression (a pro-fibrogenic marker). These findings highlight the therapeutic potential of PGC-Sec in combating liver fibrosis by enhancing mitochondrial biogenesis and function, and promoting antifibrotic processes. PGC-Sec holds promise as a novel treatment strategy for liver fibrosis.

In this paper, modelling designing and simulation of a Ward Leonard layout system is done using robust control theory. In order to increase the performance of the Ward Leonard layout system with H infinity optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers are used. The open loop response of the Ward Leonard layout system shows that the system needs to be improved. Comparison of the Ward Leonard layout system with H∞ optimal control synthesis and H infinity optimal control synthesis via gamma-iteration controllers to track a desired step speed input have been done. Finally, the comparative simulation results prove the effectiveness of the proposed Ward Leonard layout system with H infinity optimal control synthesis controller in improving the percentage overshoot and the settling time.

Succinic semialdehyde dehydrogenase deficiency (SSADH-D) is a genetic disorder that results from the aberrant metabolism of the neurotransmitter γ-amino butyric acid (GABA). The disease is caused by the impaired activity of the mitochondrial enzyme succinic semialdehyde dehydrogenase. SSADH-D manifests as varying degree of mental retardation, autism, ataxia and epileptic seizures, but the clinical picture is highly heterogeneous. So far, there is no approved therapy for this disease. In this review, we briefly summarize the molecular genetics of SSADH-D, the past and ongoing clinical trials and the emerging features of the molecular pathogenesis, including redox imbalance and mitochondrial dysfunction. The main aim of this review is to discuss the potential use of further therapy approaches that have so far not been tested in SSADH-D, such as pharmacological chaperones, read-through drugs and gene therapy. Special attention will also be paid to elucidating the role of patient advocacy organizations in facilitating research and in the communication between the researchers and the patients.

Beginning in 2012, our understanding of human papillomavirus (HPV) subcellular trafficking has undergone a drastic paradigm shift. Work from multiple laboratories has revealed that HPV has evolved a unique means to deliver its viral genome (vDNA) to the cell nucleus, relying on a myriad of host cell proteins and processes. The major breakthrough finding from these recent endeavors was the realization of L2-dependent utilization of cellular sorting factors for the retrograde transport of vDNA away from degradative endo/lysosomal compartments to the Golgi, prior to mitosis-dependent nuclear accumulation of L2/vDNA. An overview of current models of HPV entry, subcellular trafficking, and the role of L2 during initial infection is provided below, highlighting unresolved questions and gaps in knowledge.

Ultra-low radioactive titanium alloy is a promising material for the manufacture of low-background detectors, which are being developed for experiments in astroparticle physics and neutrino astrophysics. Structural titanium is manufactured on an industrial scale from titanium-sponge. The ultra-low-background titanium-sponge can be produced on an industrial scale with a contamination level of less than 1 mBq/kg of uranium and thorium isotopes. The pathways of contaminants during the industrial production of structural titanium have been analyzed. The measurements have been carried out using two methods: inductively coupled plasma spectroscopy (ICP-MS) and gamma-spectroscopy using high-purity germanium detectors (HPGe). It has been shown that the level of contamination with radioactive impurities does not increase during remelting of titanium-sponge and mechanical processing. We examined titanium-alloys samples obtained at different stages of titanium production, namely, an electrode compaction, a vacuum arc remelting with a consumable electrode (VAR), and a cold rolling of titanium-sheets. It has been found out that all studied samples will be a source of uranium and thorium contamination of the final titanium-alloys. It has been established that the only product allowed obtaining ultra-low-background titanium was the VT1-00 which is manufactured without master alloys addition..

Although most people are infected with Epstein-Barr Virus (EBV) during their lifetime, only a minority of them develop an EBV-associated malignancy. EBV acts in both direct and indirect ways to transform infected cells into tumor cells. There are multiple ways in which the EBV, host, and tumor environment interact to promote malignant transformation. This paper focuses on some of the mechanisms that EBV uses to transform the tumor microenvironment (TME) of EBV-associated gastric cancer (EBVaGC) for its benefit, including overexpression of IDO1, synergism between H pylori and EBV coinfection, and M1 to M2 switch. In this review, we expand on different modalities and combinatorial approaches to therapeutically target this mechanism.

In this work, we studied light-output properties, efficiency function as well as PSD capability of p-Terphenyl scintillator. The selected solid cylindrical scintillation detector has a size of (45 x 45) mm with PSD properties. Recently presented studies of light-output functions have been measured only for low neutron energies. Our motivation has been to determine more accurate the light output function for p-Terphenyl scintillator over a wider neutron energy range.

The negative energy solutions of the Klein-Gordon and Dirac equations have been used to define the antiparticle with the positive energy from the Feynman - Stueckelberg interpretation in the standard model based on the 4-D Minkowski space with the relative time. The negative energy solutions of the Klein-Gordon and Dirac equations are used to define the antiparticles with the negative energy in the present 3-D quantized space model. Note that all the present results are based on the 4-D Euclidean space with the absolute time (t) and relative time (t_l). Then the particle with the positive energy and antiparticle with the negative energy have the 4-D P₄ = TCP = T_cP symmetry. The continuity equations are derived from the Klein-Gordon, Dirac and Schrodinger equations. The Klein-Gordon and Schrodinger equations with the potential barriers are solved. The Klein paradox is explained by using the pair production of the electron with the positive energy and positron with the negative energy under the P₄ = _TcP symmetry, The effective velocity ( c_eff=√2 " c " ) and effective energy ("Etl =" √2 E ) along the relative time axis (ctl) give the relative time momentum of "p_tl"=E_tl/c_eff =(√2 E)/(√2 c)=E/c=p_t=p_x. This indicates that the photons with the energy of E have the constant photon velocity of c and the constant photon momentum of "ptl"=E_tl/c_eff =(√2 E)/(√2 c)=E/c=p_t=p_x. For the negative energy particles, the space momentum directions are opposite to the particle velocity directions because the energy is negative. And the matter collapse to the photons at the very high particle velocity is discussed from the length expansion. It is, for the first time, proposed that the gamma ray burst is originated from the matter collapse to the photons near the black hole. Also, the wave function collapse is explained from the length expansion. The wave function collapse takes place when the measurement makes the particle velocity to be zero. It is concluded that the negative energy solutions of the Klein-Gordon and Dirac equations support the existence of the partner antimatter universe with the negative energy and negative time direction. Our matter universe has the positive energy and the positive time direction.

Rapid search and localization for nuclear sources can be an important aspect in preventing human harm from illicit material in dirty bombs or from contamination. In the case of a single mobile radiation detector, there are numerous challenges to overcome such as weak source intensity, multiple sources, background radiation, and the presence of obstructions, i.e., a non-convex environment. In this work, we investigate the sequential decision making capability of deep reinforcement learning in the nuclear source search context. A novel neural network architecture (RAD-A2C) based on the actor critic (A2C) framework and a particle filter gated recurrent unit for localization is proposed. Performance is studied in a randomized 20 x 20 m convex and non-convex environment across a range of signal-to-noise ratio (SNR)s for a single detector and single source. RAD-A2C performance is compared to both an information-driven controller that uses a bootstrap particle filter and to a gradient search (GS) algorithm. We find that the RAD-A2C has comparable performance to the information-driven controller across SNR in a convex environment and at lower computational complexity per action. The RAD-A2C far outperforms the GS algorithm in the non-convex environment with greater than 95% median completion rate for up to seven obstructions.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z_p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

The main aim of this paper is to set some correlations between Boole polynomials and p-adic gamma function in conjunction with p-adic Euler contant. We develop diverse formulas for p-adic gamma function by means of their Mahler expansion and fermionic p-adic integral on ℤ_{p}. Also, we acquire two fermionic p-adic integrals of p-adic gamma function in terms of Boole numbers and polynomials. We then provide fermionic p-adic integral of the derivative of p-adic gamma function and a representation for the p-adic Euler constant by means of the Boole polynomials. Furthermore, we investigate an explicit representation for the aforesaid constant covering Stirling numbers of the first kind.

The ability of recombinant, SARS-CoV-2 Spike (S) protein to modulate the production of two COVID-19 relevant, pro-inflammatory cytokines (IL-6 and IFN-γ) in PBMC cultures of healthy, pre-Covid-19 subjects was investigated. We observed that cytokine production was largely and diversely modulated by the S protein depending on antigen or mitogen stimulation, as well as on the protein source, insect (S-in) or human (S-hu) cells. While both proteins co-stimulated cytokine production by polyclonally CD3-activated T cells, PBMC activation by the mitogenic lectin Concanavalin A (Con A) was up modulated by S-hu protein and down-modulated by S-in protein. These modulatory effects were likely mediated by the S glycans as demonstrated by direct Con A-S binding experiments and use of yeast mannan as Con A binder. While being ineffective in modulating memory antigenic T cell responses, the S proteins and mannan were able to induce IL-6 production in unstimulated PBMC cultures and upregulate the expression of Mannose Receptor (CD206), a marker of anti-inflammatory M2 macrophage. Our data point to a relevant role of N-glycans, particularly N-mannosidic chains, decorating the S protein in the immunomodulatory effects here reported. These novel biological activities of the S glycan ectodomain may add to the comprehension of Covid-19 pathology and immunity to SARS-CoV-2.

We previously showed that mice with knockout in the peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PPARGC1A) gene encoding the PGC-1a protein and nuclear factor erythroid 2 like 2 (NFE2L2) gene, showed some features of the age-related macular degeneration (AMD) phenotype. To further explore the mechanism behind the involvement of PGC-1a in AMD pathogenesis we used young (3-month) and old (12-month) mice with knockout in the PPARGC1A gene and age-matched wild-type (WT) animals. An immunohistochemical analysis showed age-dependent different expression of markers of oxidative stress defense, senescence and autophagy in the retinal pigment epithelium of KO animals as compared with their WT counterparts. Multivariate inference testing showed that senescence and autophagy proteins had the greatest impact on the discrimination between KO and WT 3-month animals, but proteins of antioxidant defense also contributed to that discrimination. A bioinformatic analysis showed that PGC-1a might coordinate the interplay between genes encoding proteins involved in antioxidant defense, senescence and autophagy in the aging retina. These data support importance of PGC-1a in AMD pathogenesis and confirm the utility of mice with PGC-1a knockout as an animal model to study AMD pathogenesis.

In this paper, we introduce the (ρ,q)-analogue of the p-adic factorial function. By utilizing some properties of (ρ,q)-numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic (ρ,q)-gamma function by means of the mentioned factorial function. We investigate several properties and relationships belonging to the foregoing gamma function, some of which are given for the case p = 2. We also derive more representations of the p-adic (ρ,q)-gamma function in general case. Moreover, we consider the p-adic (ρ,q)-Euler constant derived from the derivation of p-adic (ρ,q)-gamma function at x = 1. Furthermore, we provide a limit representation of aforementioned Euler constant based on (ρ,q)-numbers. Finally, we consider (ρ,q)-extension of the p-adic beta function via the p-adic (ρ,q)-gamma function and we then investigate various formulas and identities.

In this paper, we investigate several relations for p-adic gamma function by means of their Mahler expansion and fermionic p-adic q-integral on ℤ_{p}. We also derive two fermionic p-adic q-integrals of p-adic gamma function in terms of q-Boole polynomials and numbers. Moreover, we discover fermionic p-adic q-integral of the derivative of p-adic gamma function. We acquire a representation for the p-adic Euler constant by means of the q-Boole polynomials. We finally develop a novel, explicit and interesting representation for the p-adic Euler constant including Stirling numbers of the first kind.

In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on ℤ_{p} of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

This study investigated the impact of seven-strain probiotic supplementation on the frequency of T helper 17 (Th17) cells, regulatory T (T-reg) cells, Treg/Th17 ratio, and their gene expression in individuals with severe traumatic brain injury (STBI). Probiotics can influence the gut microbiota, modulate the immune response, and prevent or alleviate certain immune diseases. However, it is necessary to clarify whether probiotics can effectively impact Th cells in STBI patient. Despite the great attention to improving the immune system in most diseases, there is currently no accurate mechanism for the use of probiotics in diseases with damage to the head injury, which can be a basis for the use of probiotics. The primary objective of this study is to address this research gap. The present study was a randomized, double-blind, placebo-controlled trial that enrolled 48 STBI patients. They were treated with probiotics or placebo: 4 capsule/day for 14 days. The pre- and post-study evaluation included examining the frequency of Treg, Th17 cells, as well as the expression of associated immunological parameters (Foxp3 and RORγt) and Treg/Th17 ratio in both groups. No significant differences were found between the two groups in terms of subject characteristics (P>0.05). GCS scores at 14 days were significantly higher in the probiotic compared to the placebo group. The probiotic group showed a significant decrease in Th17 cell and RORγt gene expression (P = 0.022 and P< 0.001, respectively), a notable increase in T-reg and FoxP3 gene expression (P= 0.025 and P< 0.001, respectively), and a higher Treg/Th17 ratio compared to the placebo group. Our study provides promising evidence of the beneficial effects of seven-strain probiotic supplementation on Th cells in individuals with STBI.

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function.

The combination of interstitial hyperthermia treatment (IHT) with high dose rate brachytherapy (HDR-BT) for prostate cancer treatment and has the potential to improve clinical outcome, since it highly enhances the efficiency of cell kill, especially when applied simultaneously. Therefore, we have developed the ThermoBrachy applicators. To effectively apply optimal targeted IHT, treatment planning is considered essential. However, treatment planning in IHT is rarely applied since it is regarded difficult to accurately calculate the deposited energy in the tissue in a short enough time for clinical practice. In this study, we investigated various time-efficient methods for fast computation of the electromagnetic (EM) energy deposition resulting from the ThermoBrachy applicators. Initially, we investigated the use of an electro-quasistatic solver. Next, we extended our investigation to the application of geometric simplifications. Furthermore, we investigated the validity of the superpositioning principle, which can enable adaptive treatment plan optimization without the need for continuous recomputation of the EM field. Finally, we evaluated the accuracy of the methods by comparing them to the golden standard Finite-Difference Time-Domain calculation method using gamma-index analysis. The simplifications considerably reduced the computation time needed, improving from &gt;12 h to a few seconds. All investigated methods showed excellent agreement with the golden standard by showing a &gt;99% passing rate with 1%/0.5 mm Dose Difference and Distance-to-Agreement criteria. These results allow the proposed electromagnetic simulation method to be used for fast and accurate adaptive treatment planning.

We know that the classical Mittag-Leffler function play an important role as solution of fractional order differential and integral equations. We introduce the j-generalized p - k Mittag-Leffler function. We evaluate the second order differential recurrence relation and four different integral representations and introduce a homogeneous linear differential equation whose one of the solution is the j-generalized p-k Mittag-Leffler function. Also we evaluate the certain relations that exist between j-generalized p - k Mittag-Leffler function and Riemann-Liouville fractional integrals and derivatives. We evaluate Mellin-Barnes integral representation of j-generalized p-k Mittag-Le er Function. The relationship of j-generalized p-k Mittag-Leffler Function with Fox H-Function and Wright hypergeometric function is also establish. we obtained its Euler transform, Laplace Transform and Mellin transform. Finally we derive some particular cases.

In this paper, we derive multifarious relationships among the two types of higher order q-Daehee polynomials and p-adic gamma function via Mahler theorem. Also, we compute some weighted p-adic q-integrals of the derivative of p-adic gamma function related to the Stirling numbers of the both kinds and the q-Bernoulli polynomials of order k.

Like all RNA viruses, SARS-CoV-2 shows high mutation rate, which has led to the emergence of new variants. Among them, Gamma and Delta developed at the turn of 2020-2021 in Amazonas and India, two ecoregions characterized by hot-humid weather, very similar to that of the summer season due to climate change in Italy, the first Western country to have been hit hard by COVID-19 and to experience lockdown restrictions in a democratic framework of 58,85 million people. Methods: during the state of national health emergency and the Draghi government, the Civil Defense Department daily released the aggregate data coming from the Ministry of Health, the Higher Institute of Health, the Independent Provinces and the Italian Regions, in order to inform about the pandemic situation in Italy. Among these data there were the number of deaths, hospitalizations in intensive care units (ICU), non-ICU patients, contagions, and performed swabs. By means of a team effort, we have collected and elaborated all these data, comparing COVID-19 pandemic in Italy during the summers 2020 (following the nationwide lockdown), 2021 and 2022. Results: from summer 2020 (before mass vaccination) to summers 2021 (after primary mass vaccination) and 2022 (after booster mass vaccination) all pandemic trend indicators have showed a sharp worsening in Italy. COVID-19 deaths increased by ≈298% and ≈834%, ICU hospitalizations by ≈386% and ≈310%, non-ICU hospitalizations by ≈224% and ≈600%, contagions by ≈627% and ≈6.850% (i.e. ≈68,50 times), swabs by ≈354% and ≈370%, and the mean positivity rate passed from ≈1% to ≈2% and ≈20%, respectively. Conclusions: SARS-CoV-2 can be transmitted in any climate, including areas with hot and humid weather, and the emergence of variants adapted to hot-humid climate may result in summer COVID-19 outbreaks, even in neither tropical nor subtropical countries. Although COVID-19 vaccines can confer cross-protection against newly emerging variants, this cross-immunity is obviously not absolute but limited, also taking into account that vaccine protection wanes considerably after 6 months. It follows that a subject vaccinated at the beginning of winter will not be completely covered in the height of summer, without forgetting the unvaccinated. As a final remark, the long nationwide lockdown made it possible to flatten SARS-CoV-2 circulation and, therefore, its negative impact on Italy during summer 2020.

Gamma-aminobutyric acid (GABA) and glycine act as inhibitory neurotransmitters. Three types of inhibitory neurons and terminals, GABAergic, GABA/glycine co-releasing, and glycinergic, are orchestrated in the spinal cord neural circuits and play key roles in the regulation of pain, locomotive movement, and respiratory rhythms. Herein, we first describe GABAergic and glycinergic transmission and inhibitory networks, which consist of three types of terminals, in the mature mouse spinal cord. Second, we describe the developmental formation of GABAergic and glycinergic networks, with specific focus on the differentiation of neurons, formation of synapses, maturation of removal systems, and changes in their action. GABAergic and glycinergic neurons are derived from the same domains of the ventricular zone. Initially, GABAergic neurons are differentiated and their axons form synapses. Some of these neurons remain GABAergic in lamina I and II. Many of GABAergic neurons convert to co-releasing state. The co-releasing neurons and terminals remain in the dorsal horn, whereas many of co-releasing ones ultimately become glycinergic in the ventral horn. During the development of terminals and the transformation from radial glia to astrocytes, GABA and glycine receptor subunit compositions markedly change, removal systems mature, and GABAergic and glycinergic action shifts from excitatory to inhibitory.

Recently, Shehata et al. [37] introduced the r+1Rs(B;C; z) matrix function and established some properties. The aim of this study established to devote and derive certain basic properties including analytic properties, recurrence matrix relations, dierential properties, new integral representations, k- Beta transform, Laplace transform, fractional k-Fourier transform, fractional integral properties, the k-Riemann{Liouville and k-Weyl fractional integral and derivative operators an extended version of r+1Rs;k matrix function. We establish its relationships with other well known special matrix functions which have some particular cases in the context of three parametric Mittag-Leer matrix function, k- Konhauser and k-Laguerre matrix polynomials. Finally, some special cases of the established formulas are also discussed.