One objective of this paper is to investigate bifurcation of solutions of Ornstein-Zernike equation in liquid state theory for the gas-liquid coexistence region of simple fluids. The analysis uses a discrete form of the Ornstein-Zernike equation in real space, together with a closure relation which provides nearly self consistent thermodynamic properties of fluids governed by interaction potentials like the Lennard-Jones potential. Accurate asymptotic forms of correlation functions are incorporated in the real space algorithm so as to mitigate the influence of cutoff length used in the discrete approximations. It is found that there is no spinodal on the vapor side on a sub-critical isotherm. But there are fold bifurcation points on the vapor and liquid sides together with a 'no-real-solution-region' in between. This is followed by a region of negative compressibility extending up to the spinodal on the liquid side. The emerging picture is quite similar to that in the case of the hypernetted-chain-closure. It is also found that complex solutions connect the physical solutions that exist outside the 'no-real-solution-region' as well as in region of negative compressibility. The second objective of the paper, in the light of bifurcation scenario, is to evolve an interpretation of the coupling-parameter expansion of correlation functions pertaining to the region of negative compressibility. It is shown that the expansion provides an accurate description of results of the restricted ensembles, implied in mean field theories and simulation methods. Bifurcation of singlet density to inhomogeneous distributions at a spinodal is also established using a simple equation, which uses the direct correlation function. Thus the paper reestablishes the fact that restriction to a homogeneous singlet density is the root cause of all inconsistencies found in the gas-liquid coexistence region.

Prereactive complexes in noncovalent organocatalysis are sensitive to the relative chirality of the binding partners and to hydrogen bond isomerism. Both effects are present when a transiently chiral alcohol docks on a chiral α-hydroxy ester, turning such 1:1 complexes into elementary, non-reactive model systems for chirality induction in the gas phase. With the help of linear infrared and Raman spectroscopy in supersonic jet expansions, conformational preferences are investigated for benzyl alcohol in combination with methyl lactate, also exploring p-chlorination of the alcohol and the achiral homolog methyl glycolate to identify potential London dispersion and chirality effects on the energy sequence. Three of the four combinations prefer barrierless complexation via the hydroxy group of the ester (association). In contrast, the lightest complex shows predominantly insertion into the intramolecular hydrogen bond, like the analogous lactate and glycolate complexes of methanol. The experimental findings are rationalized with computations and a uniform helicality induction in the alcohol by the lactate is predicted, independent on insertion into or association with the internal lactate hydrogen bond. p-Chlorination of benzyl alcohol has a stabilizing effect on association, because the insertion motif prevents a close contact between the chlorine and the hydroxy ester. After simple anharmonicity and substitution corrections, the B3LYP-D3 approach offers a fairly systematic description of the known spectroscopic data on alcohol complexes with α-hydroxy esters.

The work is devoted to the study of a family of linear initial value problems of partial differential equations in the complex domain, dealing with two complex time variables. The use of a truncated Laplace-like transformation in the construction of the analytic solution allows to overcome a small divisor phenomenon arising from the geometry of the problem and represents an alternative approach to the one proposed in a recent work by the first two authors. The result leans on the application of a fixed point argument and the classical Ramis-Sibuya theorem.

A family of linear singularly perturbed Cauchy problems is studied. The equations defining the problem combine both partial differential operators together with the action of linear fractional transforms. The exotic geometry of the problem in the Borel plane, involving both sectorial regions and strip-like sets, gives rise to asymptotic results relating the analytic solution and the formal one through Gevrey asymptotic expansions. The main results lean on the appearance of domains in the complex plane which remain intimately related to Lambert W function, which turns out to be crucial in the construction of the analytic solutions. On the way, an accurate description of the deformation of the integration paths defining the analytic solutions and the knowledge of Lambert W function are needed in order to provide the asymptotic behavior of the solution near the origin, regarding the perturbation parameter. Such deformation varies depending on the analytic solution considered, which lies in two families with different geometric features.

Recently it was found from Cassini data that the mean recession speed of Titan from Saturn is v = 11.3 ± 2.0 cm/yr which corresponds to a tidal quality factor of Saturn Q ≈ 100 while the standard estimate yields Q ≥ 6 · 10⁴ . It was assumed that such a large speed v is due to a resonance locking mechanism of five inner mid-sized moons of Saturn. In this paper, we show that an essential part of v may come from a local Hubble expansion, where the Hubble-Lemaˆıtre constant H0 recalculated to the Saturn-Titan distance D is 8.15 cm/(yrD). Our hypothesis is based on many other observations showing a slight expansion of the Solar system and also of our Galaxy at a rate comparable with H0. We demonstrate that the large disproportion in estimating the Q factor can be just caused by the local expansion effect. [Accepted for publication in "Gravitation and Cosmology". The paper is to appear in Vol. 28, Issue 2 (2022) of the journal Gravitation and Cosmology.]

Light-colored and transparent polyimide (PI) films with good high-temperature dimensional stability are highly desired for advanced optoelectronic applications. However, in practice, the simultaneous achievement of good optical and thermal properties in one PI film is usually difficult due to the inter-conflicting molecular design for the polymers. In the present work, a series of PI-SiO2 nanocomposite films (ABTFCPI) were developed based on the PI matrix derived from hydrogenated pyromellitic anhydride (HPMDA) and an aromatic diamine containing benzanilide and trifluoromethyl substituents in the structure, 2,2'-bis(trifluoromethyl)-4,4'-bis[4-(4-aminobenzamide)]biphenyl (ABTFMB). The inorganic SiO2 fillers were incorporated into the nanocomposite films with the form of colloidal nanoparticles dispersed in the good solvent of N,N-dimethylacetamide (DMAc) for the PI matrix. The derived ABTFCPI nanocomposite films showed good film-forming ability, flexible and tough nature, good optical transparency, and good thermal properties with the loading amounts of SiO2 up to 30 wt% in the system. The ABTFCPI-30 film with the SiO2 content of 30 wt% in the film showed the optical transmittance of 79.6% at the wavelength of 400 nm (T400) with a thickness of 25 μm, the yellow index (b*) of 2.15, and the 5% weight loss temperatures (T5%) of 491 oC, which are all comparable to those the pristine ABTFCPI-0 matrix without filler (T400=81.8%; b*=1.77; T5%=492 oC). Meanwhile, the ABTFCPI-30 film exhibited obviously enhanced high-temperature dimensional stability with the linear coefficients of thermal expansion (CTE) of 25.4×10-6/K in the temperature range of 50 to 250 oC, which is much lower than that of the AMTFCPI-0 film (CTE=32.7×10-6/K).

The ordered Ca3TaGa3Si2O14 and disordered La3Ga5SiO14 crystals of the lantangallium silicate family were grown by the Czochralski method. The independent coefficients of thermal expansion of crystals αc and αa were determined by X-ray powder diffraction based on the analysis of X-ray diffraction spectra measured in the temperature range of 25÷1000°C. It is shown that in the temperature range of 25÷800°C the thermal expansion coefficients are linear. At temperatures above 800°C there is a nonlinear character of the thermal expansion coefficients associated with a decrease in the Ga content in the crystal lattice of the lantangallium silicate family crystals.

This article reports new measurements of laser-induced plasma hypersonic expansion measurements of diatomic molecular cyanide (CN). Focused, high-peak power 1064-nm Q-switched radiation of the order of 1 TW/cm² generates optical breakdown plasma in a cell containing a 1:1 molar gas mixture of N₂ and CO₂ at a fixed pressure of 1.1 × 10⁵ Pascal and in a 100 ml/min flow of the mixture. Line-of-sight (LOS) analysis of recorded molecular spectra indicate the outgoing shockwave at expansion speeds well in excess of Mach number 5. Spectra of atomic carbon confirm an increased electron density near the shock wave, and equally, molecular CN spectra reveal higher excitation temperature near the shockwave. The results are consistent with corresponding high-speed shadow graphs obtained by visualization with an effective shutter speed of five n anosecond. In addition, LOS analysis and application of integral inversion techniques allow inferences about the spatio-temporal distribution of the plasma.

Energy storage systems (ESSs) are the key elements to improve the operation of power systems. On the other hand, these elements challenge the power system planners. The difficulties arise as a result of the ESSs' economic and technological features. The cycle life of ESSs is a critical aspect that influences the choices made during expansion planning processes. In this manuscript, we have focused on a new model for the expansion planning of ESSs considering the impacts of technical properties, such as the cycle life and depth of discharge. For this purpose, the proposed model consists of the hourly operation planning of ESSs in the sample days of year. A new indicator is proposed to determine the daily charging/discharging cycles of ESSs. Numerical results show the ability of the proposed model to determine the optimal technology and capacity of ESSs.

We examine a family of nonlinear q-difference-differential Cauchy problems obtained as a coupling of linear Cauchy problems containing dilation q-difference operators, recently investigated by the author, and quasi-linear Kowalevski type problems that involve contraction q-difference operators. We build up local holomorphic solutions to these problems. Two aspects of these solutions are explored. One facet deals with asymptotic expansions in the complex time variable for which a mixed type Gevrey and q-Gevrey structure is exhibited. The other feature concerns the problem of confluence of these solutions as q tends to 1.

The absolute time and relative time are defined in terms of the 4-D Euclidean space. Our universe is the 3-D x₁x₂x₃ quantized photon space which follows the absolute time simultaneity when the universe moves along the absolute time axis of ct. The length expansion of Dx = gDx₀ is derived under the condition of the absolute time (ct) simultaneity. From the similarity between this length expansion of Dx = gDx₀ and the energy increasing of E = gE₀, it is assumed that the energy is proportional to the particle size of Dx. The extension of this assumption to the 4-D Euclidean space gives the new definition that the particle energy (E) is the 4-D volume. Then, the particle mass energy is defined as E= mc² = cDtDV = gE₀. The masses of the elementary particles are originated from the 4-D warped volume of the photon space because the particle is the warped photon space with the velocity of v < c. Therefore, the Higgs boson concept in the standard model (SM) is not needed in the present 3-D quantized space model (TQSM). The scalar boson with the spin of zero, photon with the spin of 1 and graviton with the spin of 2 are the two-boson states. Therefore, the observed Higgs boson is reinterpreted as the two-boson state of the scalar boson with the spin of zero. The cosmic muon observation and twin paradox are explained by using the absolute time and relative time. The relative time is the observed time in the twin paradox and cosmic muon observation. In the twin paradox, a person who travels the long distance is more aged than a person on the earth in terms of the relative time ages because of the space and time conversion effect (STCE effect) of the moving space distance (x). But twins are in the same ages in terms of the absolute time without STCE effect. The fast-moving cosmic muon has the expanded half-life from the time expansion of the relative time. Also, the quantum entanglement and Pauli exclusion principle are explained. The quantum base of the photon space line connects two entangled particles. Two particles and quantum base system is fluctuated along the absolute time axis by the time clicking when one particle is measured. Another particle is instantly selected by the time clicking. This is called as the quantum entanglement. The photons which are the flat photon space with the constant speed of c along the space axis and absolute time axis have the 4-D photon velocity of c_eff = 2^0.5 c. Total 10-D Euclidean space including three 3-D quantized spaces and one absolute time axis is required for the electric charges (EC), lepton charges (CC) and color charges (CC) of the elementary particles. The 3-D photon space is very stiff along the absolute time (ct) axis and very soft along the space axes. The Coulomb force through the photons (2EM waves) of the space fluctuations is much stronger than the Gravitational force through the gravitons (G waves) of the time fluctuations between two electrons.

The availability of sufficient amounts of form I of benzocaine has led to the investigation of its phase relationships with the other two existing forms II and III using adiabatic calorimetry, powder X-ray diffraction, and high-pressure differential thermal analysis. The latter two forms were known to have an enantiotropic phase relationship with form III stable at low-temperature and high-pressure, while form II is stable at room temperature. Using adiabatic calorimetry data, it can be concluded, that form I is the stable low-temperature, high-pressure form, which also happens to be stable at room temperature; however, form II, due to its persistence at room temperature, is still the most convenient polymorph to use in formulations. Form III presents a case of overall monotropy and does not possess any stability domain in the pressure-temperature phase diagram. Heat capacity data for benzocaine have been obtained by adiabatic calorimetry from 11 K up to 369 K above its melting point, which can be used to compare to results from in-silico crystal structure prediction.

This paper is a slightly modified, abridged version of a previous work "Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference "Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

An experimental investigation on the heat pump performance improvement equipped with the two-phase ejector called “an ejector-expansion heat pump (EEHP)” is proposed. The system performance of the EEHP is compared with a vapour-compression heat pump (VCHP). The improvement potential is determined and discussed. The heat pump test system is constructed which is based on a water-to-water heat pump. It can be experimented with both EEHP and VCHP. The two-phase ejector with the cooling load up to 2500 W is installed for experiment. The results show that the EEHP always produces a higher heating rate and COP than the VCHP throughout the specified working conditions. The heating COP is increased by 5.7-12.2% depending on the working conditions. It is also that under the same heat sink and heat source temperature, the EEHP can produce lower compressor discharge temperature and lower compressor pressure ratio than the VCHP. This is evidence that the two-phase ejector can provide better compressor working characteristics which yields a longer compressor lifetime. It is demonstrated that a key to the performance of the EEHP is the expansion pressure ratio. A larger expansion pressure ratio yields a higher improvement potential when compared with the VCHP.

Expansion of the universal space was never directly observed. It is an unproven assumption. Measurement of the gravitational redshift proves only gravitational redshift and nothing more. Gravitational redshift is proven by the Mössbauer experiment. Claiming that gravitational redshift proves universal space expansion is false because there is no causality between gravitational redshift and hypothetical expansion. Even if universal space would expand, gravitational redshift could not be taken as proof of expansion. The Doppler effect was never observed in an expanding space and claiming that cosmological redshift is partially caused by the Doppler effect caused by the expanding of space is an unproved assumption. The discovery of CMB proves only that the entire universal space radiates CMB. CMB is not proof of the existence of the recombination period.

Based on four major cosmological and astrophysical coincidences, it seems possible to develop a new model of Hubble-Hawking Universe having light speed expansion. Considering the analysis of 740 super novae data, it is possible to consider a constant rate of cosmic expansion. As there is no physical reasoning for the observed speed of light and all the cosmological observations are completely based on speed of light-by considering ‘light speed expansion’ as a characteristic nature of the universe, big bang, inflation, dark energy, quintessence and lambda term like ideal and unidentified concepts can be reviewed and relinquished at fundamental level and a practical model of expanding universe can be developed with ease and clarity. In this context, we would like to emphasize the point that, traditional definition of cosmic red shift is absolutely wrong. In terms of energy of photon, true cosmic red shift must be defined as - ratio of loss of energy in photon to the energy of photon at galaxy. We encourage the reader to see Figure 1 and Table 1 pertaining to light travel distances prepared with $\left(\frac{z}{1+z}\right)\left(\frac{c}{H_0}\right)\cong z_{new}\left(\frac{c}{H_0}\right)$. For data comparison, readers are encouraged to visit https://cosmocalc.icrar.org/ and http://www.atlasoftheuniverse.com/cosmodis.c. It may be noted that, considering 200 million solar masses as a cut off for ordinary gravity, dark matter can be considered as an effect of power law based super gravity of galactic baryonic mass. It is well believed that, Hawking’s findings about black holes are the most important contributions to physics in recent decades. Hence, we appeal the science community to recommend our Hubble-Hawking model for further research and study.

We examine a family of linear partial differential equations both singularly perturbed in a complex parameter and singular in complex time at the origin. These equations entail forcing terms which combine polynomial and logarithmic type functions in time and that are bounded holomorphic on horizontal strips in one complex space variable. A set of sectorial holomorphic solutions are built up by means of complete and truncated Laplace transforms w.r.t time and parameter and Fourier inverse integral in space. Asymptotic expansions of these solutions relatively to time and parameter are investigated and two distinguished Gevrey type expansions in monomial and logarithmic scales are exhibited.

In this paper, the new optical wave solutions of truncated M-fractional perturbed Kundu-Eckhaus model with full non-linearity are obtained by utilizing the expa function technique and modified extended tanh expansion function technique. The solutions are in the form of dark soliton, bright soliton, singular solitons and other form of solutions. The gained solutions are helpful for the further development of concerned model. The obtained results have also been presented graphically in both two-dimensional and three-dimensional formats to discuss the dynamical features as well as the parametric dependence of the constructed solutions. The study offers a highly spectacular and acceptable techniques to combine various intriguing wave demonstrations for more sophisticated models of the modern day.

This research explores the intricate relationship between gravitational and cosmic redshift phenomena, unveiling a profound understanding of how light behaves as it traverses the cosmos. The study begins with an examination of gravitational redshift, a well-established concept occurring when photons move away from massive gravitational sources, such as stars within galaxies. Gravitational redshift, expressed as λ/λ₀, manifests within the gravitational influence and extends to the boundary of the observed "zero-gravity sphere" enveloping galaxies. Within this remarkable zero-gravity sphere, gravitational effects persist, while the antigravity influence of dark energy remains negligible. As a result, gravitational redshift dominates, and cosmic redshift is notably absent within the sphere. Photons within this sphere maintain their constant speed 'c' and undergo gravitational redshift exclusively. However, as photons exit the zero-gravity sphere at a distance 'r' equivalent to the source star's radius, they encounter the onset of cosmic redshift, quantified as {(λ_obs - λ_emit)/ λ_emit}. Cosmic redshift blends with gravitational redshift, forming the effective redshift of the photon. Critically, the effective cosmic redshift surpasses gravitational redshift, illuminating a profound revelation: photons traverse a greater "light-traveled distance" than their proper distance from the source. In essence, cosmic redshift signifies that photons move across their intended distances at their intrinsic speed c, while the expanding universe introduces a relative distance expansion, influenced by antigravity. This research delves into the intricate dance between gravitational and cosmic redshift, shedding light on their remarkable implications for our comprehension of the expanding universe.

We study and describe possibilities for arities of elementary theories and of their expansions. Links for arities with respect to Boolean algebras, to disjoint unions and to compositions of structures are shown. Arities and aritizabilities are semantically characterized. The dynamics for arities of theories is described.

Persistent human papillomavirus (HPV) infection is responsible for practically all cervical and a high proportion of anogenital and oropharyngeal cancers. Therapeutic HPV vaccines in clinical development show great promise in improving outcomes for patients who mount an anti-HPV T cell response, but far from all patients elicit a sufficient immunological response. This witnesses a translational gap between animal models and human patients. Here, we investigated the potential of a new assay consisting of co-culturing vaccine-transduced dendritic cells (DCs) with syngeneic healthy human peripheral blood mononuclear cells (PBMCs) to mimic a human in vivo immunization. This new promising human ex vivo PBMC assay was evaluated using an innovative therapeutic adenovirus (Adv)-based HPV vaccine encoding the E1, E2, E6, and E7 HPV16 genes. This new method allowed us to show that vaccine-transduced DCs yielded functional effector T cells and unveiled information on immunohierarchy showing E1-specific T cell immunodominance over time. We suggest that this assay can be a valuable translational tool to complement the known animal models, not only for HPV therapeutic vaccines, and supports the use of E1 as an immunotherapeutic target. Nevertheless, the findings reported here need to be validated in a larger number of donors, and preferably in patient samples.

This paper is a slightly modified, abridged version of a previous work ``Parametric Gevrey asymptotics in two complex time variables through truncated Laplace transforms'' motivated by our contribution in the conference ``Formal and Analytic Solutions of Diff. (differential, partial differential, difference, q-difference, q-difference-differential) Equations on the Internet'' (FASnet20). It aims to clarify and give further detail at some crucial points concerning the asymptotic behavior of the solutions of the problems studied in that work.

Unlike trees, shrubs (i.e., multiple-stemmed woody plants) do not need evenly spaced large diameter structural roots and thus can spread further per unit belowground biomass. We therefore hypothesized that compared to trees, shrubs respond more to asymmetric distributions of nutrients and reach nutrient-rich patches of soil faster and with less below-ground biomass. To test these hypotheses we planted individual seedlings of shrubs (Cornus racemosa, Rhus glabra, and Viburnum dentatum) and trees (Acer rubrum, Betula populifera, and Fraxinus americana) in the centers of sand-filled rectangular boxes. In one direction we created stepwise gradients of increasing soil nutrients with slow-release fertilizer; in the other direction no fertilizer was added. Seedlings were harvested when their first root reached the plexiglass-covered fertilized end of their box; time taken as well as above- and below-ground biomass by nutrient segment were determined. There were no consistent differences between the shrubs and trees in belowground architectural plasticity (= ratio of biomass in fertilized and unfertilized volumes of soil) or in the rate and efficiency of lateral growth. Interspecific variation appeared more related to edaphic characteristics of the native habitats than to growth form. The fastest and most efficient roots were produced by the shrub (R. glabra) and the tree (B. populifolia) that are characteristic of poor soils. Root foraging by R. glabra was also facilitated by rapid rhizomatous expansion. The tested shrubs and trees did not consistently differ in nutrient foraging efficiencies or rates but further study is warranted with larger plants and more species.

The classical Einstein’s Field Equation has been derived previously by demanding that the Clausius relation dS = δQ/T holds. In this letter, we show that the semiclassical Einstein’s Field Equation can be recovered using the generalized entropy Sgen by using the non-equilibrium thermodynamics where the Clausius relation is replaced by the entropy balance relation dS = δQ/T +diS, where diS is some internal entropy. Moreover, since the quantum fields violate the classical focusing, we, therefore, have to use quantum focusing in this case. Using then Jacobson’s idea of thermodynamics of spacetime we recover the semiclassical equation of motion. We, therefore, in a sense also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.

We examine a nonlinear initial value problem both singularly perturbed in a complex parameter and singular in complex time at the origin. The study undertaken in this paper is the continuation of a joined work with A. Lastra published in 2015. A change of balance between the leading and a critical subdominant term of the problem considered in our previous work is performed. It leads to a phenomenon of coalescing singularities to the origin in the Borel plane w.r.t time for a finite set of holomorphic solutions constructed as Fourier series in space on horizontal complex strips. In comparison to our former study, an enlargement of the Gevrey order of the asymptotic expansion for these solutions relatively to the complex parameter is induced.

The principal barrier to an HIV-1 cure is the persistence of infected cells harboring replication-competent proviruses despite antiretroviral therapy (ART). HIV-1 transcriptional suppression, referred to as viral latency, is foremost among persistence determinants, as it allows infected cells to evade the cytopathic effects of virion production and killing by cytotoxic T lymphocytes (CTL) and other immune factors. HIV-1 persistence is also governed by cellular proliferation, an innate and essential capacity of CD4+ T cells that both sustains cell populations over time and enables a robust directed response to immunological threats. Yet when HIV-1 infects CD4+ T cells, this capacity for proliferation can counterproductively enable surreptitious HIV-1 propagation without the deleterious effects of viral gene expression in latently infected cells. Over time on ART, the HIV1 reservoir is shaped by both persistence determinants, with selective forces most often favoring clonally expanded infected cell populations harboring transcriptionally quiescent proviruses. Moreover, if HIV latency is incomplete or sporadically reversed in clonal infected cell populations that are replenished faster than they are depleted, such populations could both persist indefinitely and contribute to low-level persistent viremia during ART and viremic rebound if treatment is withdrawn. In this review, select genetic, epigenetic, cellular, and immunological determinants of viral transcriptional suppression and clonal expansion of HIV-1 reservoir T cells, interdependencies among these determinants, and implications for HIV-1 persistence will be presented and discussed.

This study was aim to assess the spatial-temporal trends of urban expansion with land use/land cover change dynamics over a period of 30 years in Addis Ababa. The source of data were Land sat satellite imagery freely available by the United States Geological Survey, Addis Ababa City plan map obtained from Addis Ababa city governance planning and development commission, and Ethiopia Space Science and Geospatial Agency. The data obtained were analysed by using QGIS, and ERDAS software. The finding showed that over the last thirty years Addis Ababa city was highly spreads with (Urban Expansion Intensity Index(UEII)=1.524%); building-up land increased faster (dynamic degree (K) = -6.22 and Annual Urban Expansion Rate(AUER) is 3.56. From the finding, Addis Ababa is spreading speedily.

The case of a patient with autoimmune haemolytic anaemia and an anastomosing haemangioma, is presented. The main dilemma was whether the haemangioma was the cause or the consequence of the autoimmune haemolytic anaemia and how both processes should be management. The diagnostic methods used are analytical and imaging techniques, which have not been conclusive in the diagnosis of anastomosing haemangiomas. Preoperative corticosteroid treatment does not prevent the recurrence of autoimmune haemolytic anaemia in the postoperative period. Surgical indication is established by the progression of proliferative activity, tumor enlargement and compression of the vena cava over time. Surgical resection of the tumor is the procedure used. The indication for surgical treatment of the anastomosing haemangioma and the decrease in alpha- fetoprotein after tumor resection are the most relevant results, although it increases again after a few weeks. The development of an anastomotic haemangioma may be secondary to autoimmune haemolytic anaemia. Angiogenesis resulting from the formation of erythroblastic islands at the periphery of the tumor and clonal expansions may be a mechanism to compensate for the haemolysis caused by autoimmune haemolytic anaemia

Cropland area is closely related to food production. More previous focuses were paid on impacts of extreme events on food production, but less on cropland dynamics. This study took the Farming-Pastoral Ecotone of Northern China (FPEN) as a case area, to investigate its cropland area dynamics and driving factors in view of perspectives of extreme events, environmental conditions, socioeconomic development, urban expansion, and ecological construction. We used ridge regression approach to quantify contributions of these drivers to cropland area dynamics. Results showed that cropland area increased significantly at a rate of 333.5km2/a during 1992−2020 and were spatially clustered in east of the FPEN. Impact extent and size each driving factor on cropland trend presented large spatiotemporal differences, but ecological construction (EC) had overall the greatest impact on cropland area changes, followed by urban expansion (UE). In comparison, TL10p has the smallest. UE-dominated areas increased 41.9% since 2010s, but still less than EC. Furthermore, we found that extreme events effects on cropland area trend evidently increased. Particularly, TH90p displayed the most increase (~99.4%). Cropland area changes dominated by extreme temperature events in 2010−2020 increased nearly six times than that in 1992−2010. These findings suggest that increasing impacts of extreme weather events on cropland area changes should be cautioned.

Cerebellar ataxia, neuronopathy, and vestibular areflexia syndrome (CANVAS) is caused by biallelic pathogenic expansions, or compound heterozygosity with other pathogenic variants in the RFC1 gene. CANVAS is estimated to be underdiagnosed, both because of the lack of formal diagnostic criteria and molecular challenges that translate to lesser access and high cost of routine testing. Our aim was to address the need for making CANVAS genetic testing routine, by designing a streamlined two-step PCR consisting of a short-allele screening PCR and a confirmatory PCR with fragment capillary electrophoresis detection. Exome sequencing of RFC1 was additionally foreseen to resolve potential compound heterozygosity cases. Specificity of our approach was evaluated using ataxia patients with known non-CANVAS diagnoses, and optimized using Southern blot confirmed CANVAS patients. We evaluated our approach by testing patients consecutively referred for clinically suspected CANVAS using first the two-step PCR, followed by exome sequencing. Our approach was able to accurately identify negative and confirm positive cases in prospectively collected suspected CANVAS patients presenting with at least three typical clinical signs. The proposed testing approach provides an alternative method able to clearly distinguish between CANVAS negative and positive cases and can be easily incorporated into the genetic diagnostic laboratory workflow.

We investigate a family of nonlinear partial differential equations which are singularly perturbed in a complex parameter and singular in a complex time variable at the origin. These equations combine differential operators of Fuchsian type in time and space derivatives on horizontal strips in the complex plane with a nonlocal operator acting on the complex parameter known as the formal monodromy around 0. Their coefficients and forcing terms comprise polynomial and logarithmic type functions in time and are bounded holomorphic in space. A set of logarithmic type solutions are shaped by means of Laplace transforms relatively to time and parameter and Fourier integrals in space. Furthermore, a formal logarithmic type solution is modeled which represents the common asymptotic expansion of Gevrey type of the genuine solutions with respect to the complex parameter on bounded sectors at the origin.

We present a novel method for online measurement of multi-point opening distances of midpalatal suture during rapid palatal expansion (RPE) using fiber optic Fabry-Perot (F-P) sensors. The sensor consists of an optical fiber with a cut flat end face and an optical reflector, which are implanted into the palatal base structure of an expander and is capable of measuring the precise distance between two optical reflective surfaces. As a demonstration, a 3D printed skull model containing the maxilla and zygomaticomaxillary complex (ZMC) was produced and a miniscrew-assisted rapid palatal expander (MARPE) with two guide rods was used to generate the midpalatal suture expansion. The reflected spectrums of the sensors were used to dynamically extract cavity length information for full process monitoring of expansion. The dynamic opening of the midpalatal suture during the gradual activation of the expander was measured, and a displacement resolution of 2.5 μm was demonstrated. The angle of expansion was derived and the results suggested that the midpalatal suture was opened with a slightly V type expansion of 0.03 rad at the first loading and subsequently expanded in parallel. This finding might be useful for understanding the mechanical mechanisms that lead to different types of expansion. The use of a fiber-optic sensor for mounting the rapid palatal expander facilitates biomechanical studies and experimental and clinical evaluation of the effects of RPE.

The hydrodynamics of plasma formed in the interaction of 100-ns UV KrF laser pulses with foam targets with volume densities from 5 to 500 mg/cm3 was studied. Initial and dynamic transmittance at 248-nm wavelength have been measured. At intensities about 1012 W/cm2, the propagation rates of radiation through foam targets reached 80 km/s, while plasma stream velocities from both front and rear sides of targets were approximately the same ~ 75 km/s, which confirms a volumetric absorption of radiation within the target thickness and the explosive nature of the plasma formation and expansion.

In 2021 the total world cement production was estimated at 4.1 billion tonnes and the annual CO2 emissions from cement plants reached almost 2.8 billion metric tonnes. In the last years many ef-forts have been made for manufacturing low-CO2 cements. In this regard, a great attention has been paid towards calcium sulfoaluminate (CSA) cements for both their peculiar technical prop-erties and the environmentally friendly features mainly related to their manufacturing process. Moreover, the use of blended cements composed by CSA binders and supplementary cementitious materials (SCMs) could represents a powerful tool for both reducing the CO2 footprint and pro-ducing more durable environmentally friendly materials. In this paper, the possibility of using reservoir sediments (RS), calcined at 830°C, as SCMs in blended-CSA cements was investigated. Four binders were submitted to hydration and physico-mechanical tests for curing periods com-prised in the interval 4 hours-56 days. X-ray fluorescence, X-ray diffraction and differential thermal–thermogravimetric analyses were employed as main characterization techniques. It was found that thermally treated RS are very interesting inasmuch as their utilization allows a CSA clinker dilution, thus implying both a decrease of CO2 emissions and a reduction of costs related to CSA cement production.

Electrical energy demand increase does evolve rapidly due to several socioeconomic factors such as industrialization, population growth, urbanization and of course the evolution of modern technologies in this 4th industrial revolution era. Such rapid increase in energy demand introduces a huge challenge in power system. Such has paved way for network operators to seek for alternative energy resources other than the conventional fossil fuel system. Hence, the penetration of renewable energy into the electricity supply mix has evolved rapidly in the past three decades. However, the grid system has to be well planned ahead to accommodate such increase in energy demand in the long run. Transmission Network Expansion Planning (TNEP) is a well ordered and profitable expansion of power facilities that meets the expected electric energy demand with an allowable degree of reliability. This paper proposes a TNEP model that minimises the network reinforcements, operational costs and costs of renewable energy penetrations, while satisfying the increase in demand. The problem is formulated as a mixed integer linear programming (MILP) problem. The developed model has been tested in several IEEE test systems in multi-period scenarios. The paper also carried out a detailed derivation of the new non-negative variables in terms of the power flow magnitudes, the bus voltage phase angles and the lines’ phase angles for proper mixed integer variables’ decomposition techniques. Moreover, this paper tends to provide additional recommendation in terms of which particular year (within 20 years of planning period) can the network operators install new line(s), new corridor(s) and/or additional generation capacity to the respective existing power networks. Such is achieved by running incremental periods simulations from base year through the planning horizon. The results show the efficacy of the developed model in solving the TNEP problem with a reduced and acceptable computation time even for large power grid system.

Intermediate CAG expansions in the gene ataxin-2 (ATXN2) are a known risk factor for ALS, but little is known about their role in FTD risk. Moreover, their contribution to the risk and phenotype of patients might vary in populations with different genetic background. The aim of this study was to assess the relationship of intermediate CAG expansions in ATXN2 with the risk and phenotype of ALS and FTD in the Spanish population. Repeat-Primed PCR was performed in 620 ALS and 137 FTD patients in three referral centers of Spain to determine the exact number of CAG repeats. In our cohort, ≥27 CAG repeats in ATXN2 was associated with a higher risk of developing ALS (odds ratio [OR] = 2.666 [1.471-4.882]; p = 0.0013), but not FTD (odds ratio [OR] = 1.446 [0.558-3.574]; p = 0.44). Moreover, ALS patients with ≥27 CAG repeats in ATXN2 showed shorter survival rate compared to those with &lt;27 repeats (hazard ratio [HR] 1.74 [1.18, 2.56], p = 0.005), more frequent limb onset (odds ratio [OR] = 2.34 [1.093-4.936]; p = 0.028), as well as family history of ALS (odds ratio [OR] = 2.538 [1.375-4.634]; p = 0.002). Intermediate CAG expansions of ≥27 repeats in ATXN2 are associated with ALS risk, but not with FTD, in the Spanish population. ALS patients carrying an intermediate expansion in ATXN2 show more frequent limb onset, but worse prognosis than those without expansions. In patients carrying C9orf72 expansions, the intermediate ATXN2 expansion might increase the penetrance and modify the phenotype.

We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of a suitable Abel-type transform of the function itself. Thus, the computation of N Legendre coefficients can be performed efficiently in O(NlogN) operations by means of a single Fast Fourier Transform of the Abel-type transform of f(x). We also show how the symmetries associated with the Abel-type transform can be exploited to further reduce the computational complexity. The dual problem of calculating the sum of Legendre expansions is also considered. We prove that a Legendre series can be written as the Abel transform of a suitable Fourier series. This fact allows us to state an efficient algorithm for the evaluation of Legendre expansions. Finally, numerical tests are presented to exemplify and confirm the theoretical results.

A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.

We appeal the science community to review the basic definition of wavelength dependent cosmic red shift. We would like to emphasize the point that, the true cosmic red shift must be defined as the ratio of loss in energy of photon to the energy of photon at galaxy. In terms of wavelength, photon red shift must be defined as the ratio of change in wavelength to the observed wavelength of photon. Considering the recent paper pertaining to cosmic halt authored by Cosmin Andrei, Anna Ijjas, and Paul J. Steinhardt and reviewed by Saul Perlmutter, in this paper we propose a very simple model of the universe having early stage light radius of proton seems to be equal to half the product of reduced Planck’s constant and current speed expansion and current stage quantum halt accompanied by continuous light speed rotation. In this context, representing early cosmic expansion and rotation as an outward spiral, it seems possible to consider Hubble’s law as a representation of current cosmic light speed rotation having no further expansion. To understand the current cosmic halt, we are proposing very simple and very strange atomic and nuclear relations that constitute Hubble parameter and gravitational constant. Qualitatively and quantitatively, gravitational potential energy of proton and electron separated by a distance of root mean square radius of proton. Based on uncertainty condition, it needs further study, observations and analysis. We have extended our analysis towards the microscopic coupling constants. Thus, instead of considering the cosmological variable nature of elementary physical constants, we consider the case of current or nearby cosmic halt by means of considering the equality of current cosmic variable physical constants having similar dimensions of fixed elementary physical constants and their combinations. In this connection, it is very interesting to note that, our estimated cosmic age of (2/H0) is matching with recent estimates proposed by Rajendra P Gupta and published in MNRAS.

We present a modified characteristic finite element method that exhibits second-order spatial accuracy for solving convection-reaction-diffusion equations on surfaces. The temporal direction adopted backward-Euler method, while the spatial direction employed surface finite element method. In contrast to regular domains, it is observed that the point in the characteristic direction traverses the surface only once within a brief time. Thus, the good approximation of the solution in the characteristic direction holds significant importance for the numerical scheme. In this regard, Taylor expansion is employed to reconstruct the solution beyond the surface in the characteristic direction. The stability of our scheme is then proved. A comparison is made with an existing characteristic finite element method based on face mesh. Numerical examples are provided to validate the effectiveness of our proposed method.

In this paper, we exhibit new dynamical properties of the two-mode Caudrey-Dodd-Gibbon (TMCDG) equation. This model describes the motion of dual-waves in dispersive and nonlinear media, which mainly depends on the nonlinearity and dispersion parameters. The overlapping of such two-mode waves is affected by the phase-velocity parameter. The study takes a full advantages of the Kudryashov method and of the exponential-expansion method. For the first time, dual-wave solutions are obtained for arbitrary values of the nonlinearity and dispersive factors. The graphs of the novel solutions are also provided in order to depict the waves propagation, as well as to show the influence of the parameters.

Hydrogen powered vehicles use high-pressure reservoirs from which the gas is transferred to the low-pressure fuel-cell via a classical pressure reduction valve. In these systems no expansion work is recovered and the question is addressed of the potential to increase the global efficiency by using an expansion machine between the reservoir and the electrochemical reactor. This paper investigates the feasibility of such an expansion machine, evaluates the mechanical constraints in terms of forces, torques and produced power by numeric simulation. It further evaluates the energetic contribution to the whole conversion chain from the hydrogen reservoir to the common electrical network on board. A low energy contribution of the expansion system addresses the question of the real benefit of such an investment.

The available direct gas dynamic tables provide the area ratio and the Prandtl-Meyer(P-M) angle of isentropic expansion of gas as functions of the Mach number. But finding the value of the Mach number in terms of area ratio or P-M angle requires an inverse function. Currently, the Mach number is determined by either interpolation from the direct gas dynamics tables, or the application of non-linear equation solvers using numerical methods. Both methods are approximate. In this paper inverse functions for Mach number in the form of Taylor’s series expansions are reported to develop the so-called inverse tables. The advantage of this approach is that the Mach number with a greater accuracy, referred to as nearly exact can be obtained by reading from the inverse table. In the presentation, the necessary equations and new tables that can be used by the scientific community will be disseminated. The data and computer programs are made available on GitHub through https://github.com/anillals/Inverse-gas-dynamic-tables- and-codes. A paper describing the complete mathematical steps in the derivation of the equations can be found at https://rdcu.be/dgrlf

Recently, Gohar et al. introduced a novel, local, and well-behaved fractional calculus. It possesses all the classical properties, and Its locality imposes simplicity and accuracy in modeling fractional order systems. In this article, we further develop the definitions and extend the classical properties of Gohar fractional calculus to address some of the open problems in Calculus. The fractional Gronwall's integral inequality, Taylor power series expansion, and Laplace transform are defined and applied to overcome some of the limitations in the classical integer-order calculus. The fractional Laplace transform is applied to solve Bernoulli-type logistic and Bertalanffy nonlinear fractional differential equations, and the criteria under which it can be applied to solve linear differential equations are investigated.

The holographic principle states that the information about the volume of space is stored on its boundary. Assuming this holds, we can explain the aspects of gravity. The spacetime needs to be extended to 5D to explain gravity in this context. This naturally explains the four classical tests of gravity namely the gravitational redshift, the perihelion precession, the bending of light, and the gravitational time delay. We also show a novel way in which the universe expands in an accelerated manner at late times without the need for any form of dark energy.

The growing importance of hydrogen as an energy carrier in a future decarbonized energy system has led to a surge in its production plans. However, the development of infrastructure for hydrogen delivery, particularly in the hard-to-abate sectors, remains a significant challenge. While the construction of new pipelines entails substantial investment, repurposing existing pipelines offers a cost-effective approach to jump-starting hydrogen networks. Many European countries are exploring the possibility of utilizing their current pipeline infrastructure for hydrogen transport. Yet, a critical aspect requiring extensive research is the expansion planning of these networks to accommodate increased capacity in the future. This study investigates the utilization of existing natural gas pipeline infrastructure for hydrogen transportation as a cost-saving measure. It explores two expansion strategies, namely pipeline looping and compression, for repurposing a segment of a 342 km x 36inch existing pipeline, from the Escravos – Lagos gas pipeline system (ELPS) in Nigeria, for hydrogen transport. Employing the Promax® process simulator tool, the study assesses compliance with the API RP 14E and ASME B31.12 standards for hydrogen and hydrogen-methane blends. Both expansion strategies demonstrate acceptable velocity and pressure drop characteristics for hydrogen blends of up to 40%. Additionally, the increase in hydrogen content leads to heightened compression power requirements until approximately 80% hydrogen in the blends for compression, and a corresponding extension in looping length until around 80% hydrogen in the blend for looping. Moreover, the compression option proves to be more economically viable for all investigated proportions of hydrogen blends for the PS1-PS5 segment of the Escravos – Lagos gas pipeline case study. The percentage price differentials between the two expansion strategies reach as high as 495% for a 20% hydrogen proportion in the blend. This study offers valuable insights into the technical and economic implications of repurposing existing natural gas infrastructure for hydrogen transportation.

We review time expansion wave theory and refine our model showing it to accurately match observed cosmological luminosity data. The theory augments general relativity to create a container within which quantum effects can be explained by treating time as an artefact of a fourth spatial dimension that we observe as the expansion of the universe. This leads us to explain mass creation, the speed of light limit, gravity, black holes without singularities and other macroscopic effects. Our model leads to an expansion velocity of 6.87 0.36 × 106 ms-1, which results in a Hubble expansion rate constant of 71.3 3.7 km/s/Mpc. Because of the finite window of time in which we exist, an extra a degree of freedom is available leading to interesting interpretations at the subatomic level. At this size range, then a spin is allowed within the time dimension explaining why wave particle duality occurs and explains the electromagnetic force and other quantum mechanical properties. It provides a solution to the double slit conundrum and can explain how quantum entangled partners can behave in a quantum way and pass seemingly time-defying information. The potential quantitative origin of the fine structure constant which governs the size of the electromagnetic force is also strongly indicated by this theory.

Abstract: rainfall is the main driver of soil erosion. With the daily rainfall, riverine flow discharge and sediment load in the upper Lianjiang River watershed from 1990 to 2020, extreme rainfall events were defined by the 95th percentile method and minimum event interval time (MIT), change trends and mutations of yearly rainfall, riverine flow discharge and sediment load were identified using the Mann-Kendall test, then the optimum lag response time and antecedent rainfall were investigated with the multiple linear regression. The results showed that (1) the sediment changed significantly and abruptly in 1995 due to the expansion of the garden land. (2) Compared with ordinary rainfall, extreme rainfall events explained more variations of riverine flow and sediment with a higher degree, and had a more significant effect on the lag time of runoff and sediment. (3) Garden land expansion in extreme rainfall scenarios resulted in longer lag times for runoff and sediment and decreased demand for antecedent rainfall with more pre-event time. Therefore, taking the rainfall event as a breakthrough, analyzing the antecedent rainfall and the lag response of riverine flow discharge and sediment load is conducive to revealing the response mechanism of riverine flow discharge and sediment load and improving the simulation accuracy of riverine flow and sediment under extreme rainfall condition, thus help for the soil erosion control under extreme rainfall.

Aspergillus fumigatus is a ubiquitous, critical priority human fungal pathogen. Despite its clinical importance, there is limited knowledge regarding the variations of the genome within mitochondria, the powerhouse organelle within eukaryotic cells. In this study, we leveraged publicly available raw, whole genome sequence data from 1939 isolates to investigate the variations in the mitochondrial genomes of A. fumigatus. These isolates were isolated from 22 countries on six continents, as well as from outer space and from within the International Space Station. In total, our analysis revealed 39 mitochondrial single nucleotide polymorphisms (mtSNPs) within this global sample and together, these 39 mtSNPs grouped the 1939 isolates into 79 mitochondrial multilocus genotypes (MLGs). Among the 79 MLGs, 39 were each distributed in at least two countries and 30 were each shared by at least two continents. The two most frequent MLGs were also broadly distributed: MLG11 represented 420 isolates from 11 countries and four continents and while MLG79 represented 418 isolates from 18 countries and five continents, consistent with long-distance dispersals of mitogenomes. Our population genetic analyses of the mtSNPs revealed limited differentiation among continental populations but highly variable genetic differences among national populations, largely due to localized clonal expansions of different MLGs. Phylogenetic analysis and Discriminant Analysis of Principal Components of mtSNPs suggested the presence of at least three mitogenome clusters. Linkage disequilibrium, Index of Association, and phylogenetic incompatibility analyses collectively suggested evidence for mitogenome recombination in natural populations of A. fumigatus. In addition, sequence read depth analyses revealed an average ratio of ~20 mitogenomes per nuclear genome in this global population but the ratios varied among strains within and between certain geographic populations. Together, our results suggest evidence for organelle dynamics, genetic differentiation, recombination, and both widespread and localized clonal expansion of the mitogenomes in the global A. fumigatus population.

Paratemporal methods based on tree expansion have proven to be effective in efficiently generating trajectories of stochastic systems. However, combinatorial explosion of branching arising from multiple choice points presents a major hurdle that must be overcome to implement such techniques. In this paper we tackle this scalability problem by developing a systems theory-based framework covering both conventional and proposed tree expansion algorithms for speeding up discrete event system stochastic simulations while preserving desired accuracy. An example is discussed to illustrate the tree expansion framework in which a discrete event system specification (DEVS) Markov stochastic model takes the form of a tree isomorphic to a free monoid over the branching alphabet. We derive the computation times for baseline, non-merging, and merging tree expansion algorithms to compute the distribution of output values at any given depth. The results show the remarkable reduction from exponential to polynomial dependence on depth effectuated by node merging. We relate these results to the similarly reduced computation time of binomial coefficients underlying Pascal’s triangle. Finally, we discuss application of tree expansion to estimating temporal distributions in stochastic simulations involving serial and parallel compositions with potential real world use cases.

The traditional approach of considering the probability distribution of rain attenuation leads to overdesign the power margin of data channels. We have first recalled a method, proposed in 2016, which with a small power margin, bandwidth expansion and variable symbol rate avoids overdesign and can transfer the same data volume as if the link were in clear–sky conditions. It is charaterized only by the link mean efficiency 0≤η≤1, suitably defined. It is usefull only if: (a) data must be downloaded also when it is raining; (b) real–time communication is not strictly required. We have applied it to the links of GeoSurf satellite constellations by simulating rain attenuation time series at 80 GHz (mm–wave) with the Synthetic Storm Technique, from rain-rate time series recorded on–site, at sites located in different climatic regions. The power margin to be implemented ranges from 2.0 dB to 7.4 dB – well within the current technology – regardless the instantaneous rain attenuation. The clear–sky bandwidth is expanded 1.75 to 2.80 times, not large per se, but it may challenge current technology if the clear–sky bandwidth is already large.

Nuclear fusion reactors are composed by several complex components whose behaviour may be not certain a priori. This uncertainty may have a significant importance in the evolution of fault transients in the machine, causing unexpected damages to its components. For this reason a suitable method for the uncertainty propagation during those transient is required. The Monte Carlo method would be the reference option, but it is, in most of the cases, not applicable due to the large amount of required simulations to be repeated. In this context the Polynomial Chaos Expansion has been considered as a valuable alternative. It allows to create a surrogate model of the original one in terms of orthogonal polynomials. Then, the uncertainty quantification is performed repeatedly calling this much simpler and faster model. Using the fast current discharge in the Divertor Tokamak Test Toroidal Field (DTT TF) coils as a reference scenario, this method has been applied: the uncertainty on the parameters of the Fast Discharge Unit (FDU) varistor disks is propagated to the simulated electrical and electro-magnetic relevant effects. Eventually two worst case scenarios have been analyzed from the thermal-hydraulic point of view with the 4C code, simulating a fast current discharge as a consequence of a coil quench. Eventually it has been demonstrated that the uncertainty on the inputs (varistor parameters) strongly propagates obtaining a wide range of possible scenarios in case of accidental transients. This result underlines the necessity to take into account and propagate all possible uncertainties in the design of a fusion reactor, according to the Best Estimate Plus Uncertainty approach.

We delve into the intricate dynamics governing anisotropic fluids within the cosmological paradigm, elucidating the nuanced influence of conformal anomalies upon the stress-energy tensor. Through the presentation of a sophisticated theoretical framework, we seamlessly intertwine unconventional fluidic properties with profound cosmological considerations, thereby augmenting and refining our comprehension of the primordial universe.

We examine a linear q-difference differential equation which is singular in complex time t at the origin. Its coefficients are polynomial in time and bounded holomorphic on horizontal strips in one complex space variable. The equation under study represents a q-analog of a singular partial differential equation, recently investigated by the author, which comprises Fuchsian operators and entails a forcing term that combines polynomial and logarithmic type functions in time. A sectorial holomorphic solution to the equation is constructed as a double complete Laplace transform in both time t and its complex logarithm log t and Fourier inverse integral in space. For a particular choice of the forcing term, this solution turns out to solve some specific nonlinear q-difference differential equation with polynomial coefficients in some positive rational power of t. Asymptotic expansions of the solution relatively to time t are investigated. A Gevrey type expansion is exhibited in a logarithmic scale. Furthermore, a formal asymptotic expansion in power scale is displayed, revealing a new fine structure involving remainders with both Gevrey and q-Gevrey type growth.

Motivated by the intriguing discovery of $X(6900)$ by LHCb Collaboration, we undertake a comprehensive study of the $s\bar{s}s\bar{s}$ tetraquark system in positive parity, employing the Gaussian expansion within the chiral quark model method. We consider two structures, diquark-antidiquark ($ss$-$\bar{s}\bar{s}$) structure and meson-meson ($s\bar{s}$-$s\bar{s}$)strcuture, encompassing all conceivable color and spin configurations. Despite the absence of bound states in our calculations, we have identified potential resonant states with $J^P=0^{+}$, namely $R(0,2150)$ and $R(0,2915)$, as well as a resonant state with $J^P=1^{+}$ denoted as $R(1,2950)$, and a resonant state with $J^P=2^{+}$ denoted as $R(2,2850)$, utilizing the real-scaling method. Through a comparison of their energies and widths, we propose that $R(0,2915)$ and $R(1,2950)$ may share characteristics with $X(6900)$, while $R(0,2150)$ could be a promising experimental candidate for $f_0(2100)$. We strongly advocate for experimental investigations to shed light on the existence and properties of these resonant states.

This paper presents the tensor properties of joint probability densities on a Riemannian manifold. Initially we develop a binary data matrix to record variables' values of a large number of particles confining in a closed system at a certain time in order to retrieve the joint probability densities of related variables. By introducing the particle oriented coordinate and generalized inner product as a multi-linear operation on the basis of this coordinate, we extract the set of joint probabilities and prove them to meet covariant tensor properties on a general Riemannian space of variables. Based on the Taylor expansion of scalar field in Riemannian manifolds, it has been shown that the symmetrized iterative covariant derivatives of cumulative probability function defined on Riemannian manifold also gives the set of related joint probability densities equivalent to the aforementioned multi-linear method. We show these covariant tensors reduce to classical ordinary partial derivatives in ordinary Euclidean space with Cartesian coordinates and gives the formal definition of joint probabilities by partial derivatives of cumulative distribution function. The equivalence between symmetrized covariant derivative and generalized inner product has been concluded. Some examples of well-known physical tensors clarify that many deterministic physical variables are presented as tensor densities with an interpretation similar to probability densities.

A model of space-time is presented, whose origin is set before the appearance of any universe. It uses concepts of previous work, a central one being that the information about the laws of nature is stored locally everywhere in space such that all physical processes obey them. Since information storage is bound to matter or energy, space is assumed to consist of dark energy (DE), which thus assumes an importance far beyond its function as a stopgap for an energy deficit in our universe (U). The primordial state (PS) is a timeless and relatively large space of 3 dimensions described by a Wheeler DeWitt (WDW) equation, whose solution is interpreted as an arrangement of very many space quanta and possesses all the characteristics of the time-honored concept of the unmoved mover. The comparison of WDW solutions belonging to different mass densities of the DE favors one in which the space quanta are mini black holes, and allows the space quanta to be imagined as mass points that are kept at a distance compatible with the quantum volume by the Pauli principle or something equivalent. Triggered by an increase in probability, the PS is followed by a time-dependent state of space expansion (ES). The concomitant emergence of time occurs in a lightning huge crash, consuming almost all DE of the PS. The subsequent expansion proceeds in quantum leaps, whose huge size emerges from a WDW equation novelly derived from the time-dependent classical expansion solution, and is also used as size of the PS. Information is assumed to be geometrically stored in arrangements of space quanta similar to how genetic information is stored in DNA molecules. During space expansion information must be transferred from already existing "information quanta" to new ones. This requires time, slows down the expansion and is taken into account by a friction term in the cosmological momentum equation. Sinc e the Friedmann-Lemaître (FL) equation remains fully valid, the model can exclusively be based on recognized equations, so that the assumptions used to build it can be understood as interpretations.

This study presents an in-depth analysis of land use and land cover change on the Kerch Peninsula over a period spanning three decades. Utilizing convolutional neural networks alongside satellite imagery analysis, we have mapped and quantified the changes in land use and cover, revealing significant trends and transformations within the peninsula's landscape. The research aims to elucidate the interplay between anthropogenic activities, climatic variations, and policy interventions in shaping land cover dynamics, thereby providing insights into the environmental and socio-economic impacts of these changes. Our findings indicate a marked increase in urban expansion at the expense of natural ecosystems, including forests and wetlands, underscoring the urgent need for sustainable land management strategies. The study highlights the role of agricultural intensification and expansion in altering the peninsula's ecological balance and emphasizes the critical importance of integrating change analysis and prediction. By leveraging advanced remote sensing and GIS technologies, our analysis not only enhances the understanding of the complex dynamics driving land use and land cover change but also showcases the potential of predictive modeling in forecasting future land cover scenarios. The implications of this study extend beyond the Kerch Peninsula, offering valuable lessons for managing land use changes and conserving natural landscapes in similar regions globally.

We investigate a singularly perturbed q-difference differential Cauchy problem with polynomial coefficients in complex time and space with quadratic nonlinearity. We construct local holomorphic solutions on sectors in the complex plane with respect to the perturbation parameter with values in some Banach space of formal power series in space with analytic coefficients on shrinking domains in time. Two aspects of these solutions are addressed. One feature concerns asymptotic expansions in the parameter for which a Gevrey type structure is unveiled. The other fact deals with confluence properties as q tends to 1. In particular the built up Banach valued solutions are shown to merge in norm to a fully bounded holomorphic map in all its arguments that solves a nonlinear partial differential Cauchy problem.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights in quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows to extract high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo which enables calculations on large finite systems. Finite-size scaling can then be used to determine physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.