Background: Amyloid beta peptides (Aβ) have been identified as the main pathogenic agents in Alzheimer’s disease (AD). Soluble Aβ oligomers, rather than monomer or insoluble amyloid fibrils, show membrane-binding capacity to red blood cells (RBCs) and trigger several morphological and functional alterations in RBCs that can result in impaired oxygen transport and delivery. Since bioactive lipids have been recently proposed as potent protective agents against Aβ toxicity, we investigated the role of sphingosine-1-phosphate (S1P) in signaling pathways involved in the mechanism underlying ATP release in Aβ-treated RBCs. Methods: In RBCs following different treatments, ATP, 2,3 DPG, cAMP levels, and caspase 3 activity were determined by spectrophotometric and immunoassay. Results: S1P rescued the inhibition of ATP release from RBCs triggered by Aβ through a mechanism involving caspase-3 and restoring 2,3 DPG and cAMP levels within the cell. Conclusions: These findings reveal the molecular basis of S1P protection against Aβ in RBCs and suggest new therapeutic avenues in AD.

Weak interaction processes continue to be hot topics in fundamental physics research. In this paper, we briefly review some recent advances in the theoretical study of beta and double-beta decays that include both the nuclear and atomic part of these processes. On the nuclear side, we present a statistical approach for the computation of the nuclear matrix elements (NME) for neutrinoless double-beta (0νββ). A range of NME values, the most probable value for NME, and the associated theoretical uncertainty are given. Correlations with other related observables are shown as well. On the atomic side, we first briefly review the methods used to get the electrons’ wave functions. Further, we use them for the computation of some relevant kinematic quantities such as Fermi functions, electron spectra and angular correlation between the emitted electrons. Then, we present applications of these calculations to the experimental data analysis related to the search of the Lorentz invariance violation in two-neutrino double-beta (2νββ) decay and description of the decay rates and decay rate ratios for allowed and unique forbidden electron capture (EC) processes.

We introduce the notion of generalized contraction on dualistic partial metric spaces. A fixed point theorem for mappings satisfying above mentioned contraction is obtained. Some consequences of our result are obtained. We construct an example to demonstrate the effectiveness of our result among the corresponding results in partial metric spaces. Our results provide substantial generalizations and improvements of several well known results existing in the comparable literature. We discuss an application of our fixed point results to show the existence of solution of functional equations.

In the present study. At first, some properties of r-fuzzy soft β-closed sets are introduced on fuzzy soft topological spaces based on the paper Aygunoglu et al. (Hacet. J. Math. Stat. 2014, 43, 193-208). Also, we define the closure and interior operators with respect to the classes of r-fuzzy soft β-closed and r-fuzzy soft β-open sets, and investigate some of their properties. In addition, the concept of r-fuzzy soft β-connected sets is introduced and characterized with help of fuzzy soft β-closure operators. Thereafter, some properties of a fuzzy soft β-continuity are studied. Furthermore, we introduce and study the concepts of fuzzy soft almost (weakly) β-continuous functions, which are weaker forms of a fuzzy soft β-continuity. Also, the relationships between these classes of functions are specified with the help of some illustrative examples. Finally, we explore new types of fuzzy soft functions called, fuzzy soft β-irresolute (strongly β-irresolute, β-irresolute open, β-irresolute closed and β-irresolute homeomorphism) functions, and discuss some properties of them. Also, we show that fuzzy soft strongly β-irresolute → fuzzy soft β-irresolute → fuzzy soft β-continuity, but the converse may not be true.

Drowsiness is a main factor for various costly defects, even fatal accidents in areas such as construction, transportation, industry and medicine, due to the lack of monitoring vigilance in the mentioned areas. The implementation of a drowsiness detection system can greatly help to reduce the defects and accident rates by alerting individuals when they enter a drowsy state. This research proposes an Electroencephalography (EEG) based approach for detecting drowsiness. EEG signals are passed through a preprocessing chain composed of artifact removal and segmentation to ensure accurate detection followed by different feature extraction methods to extract the different features related to drowsiness. This work explores the use of various machine learning algorithms such as Support Vector Machine (SVM) the K Nearest Neighbor (KNN) the Naive Bayes (NB) the Decision Tree (DT) and the Multilayer Perceptron (MLP) to analyze EEG signals sourced from the DROZY database, carefully labeled into two distinct states of alertness (awake, and drowsy). Segmentation into 10-second intervals ensures precise detection, while a relevant feature selection layer enhances accuracy and generalizability. The proposed approach achieves high accuracy rates of 99.84% and 96.4% for intra (subject by subject) and inter (cross-subject) modes, respectively. SVM emerges as the most effective model for drowsiness detection in the intra mode, while MLP demonstrates superior accuracy in the inter mode. This research offers a promising avenue for implementing proactive drowsiness detection systems to enhance occupational safety across various industries.

It has been empirically observed that the upper tail of the firm size distribution follows either the Pareto distribution or the Zipf distribution, with both patterns being explained by Gibrat’s law (Gabaix, 1999). This article analyzed firm revenue data from China, spanning from 2005 to 2013, to examine the whole range of the firm size distribution. Our empirical analysis revealed that firm revenue data over these years is well fitted by a three-parameter generalized Pareto distribution, with the fitted parameters indicating a dichotomy: The size distribution of large-sized firms, namely the upper tail, is asymptotically characterized by a Pareto distribution or a Zipf distribution, whereas the size distribution of smaller and medium-sized firms is approximated by an exponential distribution. This finding suggests that Gibrat’s law should be extended to account for the emergence of a generalized Pareto distribution.

We introduce a new generalized inverse which is a natural generalization of (pseudo) right core inverse in a Banach *-algebra. We characterize this generalized inverse by using right core and quasi-nilpotent decomposition. We then present its polar-like characterization and investigate related algebraic properties. Finally, the right core-EP inverse is characterized by certain new ways.

In this paper, we present Binet's formulas, generating functions, and the summation formulas for generalized Pentanacci numbers, and as special cases, we investigate Pentanacci and Pentanacci-Lucas numbers with their properties. Also, we define Gaussian generalized Pentanacci numbers and as special cases, we investigate Gaussian Pentanacci and Gaussian Pentanacci-Lucas numbers with their properties. Moreover, we give some identities for these numbers. Furthermore, we present matrix formulations of generalized Pentanacci numbers and Gaussian generalized Pentanacci numbers.

In this paper, we introduce the notion of the generalized $w$-group inverse in a Banach algebra with proper involution. This is a natural generalization of generalized (weak) group inverse in Banach *-algebras. Many elementary properties of such new weighted generalized inverse are presented. We further establish the equivalent relations between generalized weighted group inverse and weighted generalized Drazin inverse. Related properties of generalized (weak) group inverse are extended to the wider cases.

A new generalized definition of Mersenne numbers is proposed of the form (a^n - (a-1)^n), called Global Generalized Mersenne numbers, or simply Generalized Mersenne numbers and noted GM_{a,n} where a is the base and n is the exponent, both being positive integers. The properties are investigated for prime exponents n and several theorems on Mersenne numbers regarding their congruence properties are generalized and demonstrated. In particular, it is found that, for any base a, Generalized Mersenne numbers are in general such that (GM_{a,n} - 1) are even and divisible by n, a and (a-1) for any odd prime exponent n and by (a(a-1)+1) for any prime exponent n > 5. The remaining factor is a function of triangular numbers of (a-1), specific to each prime exponent n. Four theorems on Mersenne numbers are generalized and four new theorems are demonstrated, allowing to show first, that (GM_{a,n} - 1) are divisible by 6, and more precisely GM_{a,n} are congruent to 1(mod 12) or 7(mod 12) depending on the congruence of the base a(mod 4); second, that (GM_{a,n} - 1) are divisible by 10 if n == 1(mod 4) and, if n == 3(mod 4), GM_{a,n} == 1(mod 10), or 7(mod 10) or 9(mod 10) depending on the congruence of the base a(mod 5); third, that all factors c_{i} of GM_{a,n} are of the form (2nf_{i}+1) with f_{i} natural integers such that c_{i} is prime itself or the product of primes of the form (2nj+1) with j natural integer; fourth, that for odd prime exponents n, all GM_{a,n} are periodically congruent to either +/-1\(mod 8) or +/-3(mod 8) depending on the congruence of the base a(mod 8); and fifth, that the factors of a composite GM_{a,n} is of the form (2nf_{i}+1) with f_{i} == u(mod 4) and u being either 0, 1, 2 or 3 depending on the congruence of the exponent n(mod 4) and on the congruence of the base a(mod 8). The potential use of Generalized Mersenne primes in cryptography is shortly addressed.

Statistical modeling of lifetime data plays an essential role in a wide range of practical fields, such as health and engineering. There have been a lot of studies done to develop statistical models that can better describe health data than traditional models. For the first time, we pioneer a novel family of continuous probability distributions called the generalized odd beta prime generalized (GOBP-G) family of distributions. The cumulative distribution and probability density functions of the new family are presented. A new generalization of the Weibull distribution called "generalized odd beta prime-Weibull" (GOBPW) is proposed using the pioneered GOBP-G family. The mixture representations of the new distribution are defined and derived. Some formal statistical properties of the GOBPW distribution, such as the moments, moment generating function, incomplete moments, information generating function, entropies, stress-strength function, quantile function, and order statistics, are derived. The estimation of the parameters of the proposed distribution is evaluated using the maximum likelihood estimation approach. Different cancer disease data sets, such as the bladder, head and neck, acute bone, and blood cancers, are used to illustrate the applicability and usefulness of the new model and were compared using several statistical accuracy measures with that of well-established extended Weibull distributions, which are the beta modified Weibull distribution, Kumaraswamy modified Weibull distribution, gamma generalized modified Weibull distribution, gamma log-logistic Weibull distribution, and beta log-logistic Weibull distribution. The results show that the proposed model gives better results than the competitive models. This study could guide the relevant stakeholders in choosing a suitable statistical model for the health data instead of relying on traditional models to enhance decision-making.

Motivated by empirical observations, we propose a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution (Gabaix, 2009), we find that the income distribution is described by a generalized Pareto-type distribution (GPD) with three parameters. We observe that there is a parameter /elta in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically show that, for typical market-economy countries, /elta is close to 0 significantly, such that the income distribution is characterized by a two-class pattern in which the bottom 90% of the population is approximated by an exponential distribution and the richest 1%~3% is approximated by an asymptotic power law. However, we empirically find that, for China both in planned economy period and in early stages of market reformation (from 1978 to 1990), /elta is significantly deviated from 0, such that the bottom of the population no longer conforms to an exponential distribution.

In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.

Directed energy deposition (DED) parameters were determined for near-β alloy Ti-55511 by employing statistical design of experiments (DOE) methods. Parameters resulting in fully dense freeform deposits were identified using two sequential DOEs. Single laser tracks were printed with several laser power, traverse rate, and powder feed rate settings in an initial DOE to identify promising build parameters. Capture efficiency and effective deposition rate were used to characterize and rank the single track deposits. The best parameters were then used to print solid cube with various X-Y and Z-overlaps (different hatch spacing, HS, and layer thickness, ZS) in a second DOE. Suitable deposition parameters were selected based on cube density and microstructure and were used to fabricate larger tensile samples for mechanical testing. Multiple parameter sets were found to provide dense Ti-55511 deposits with acceptable mechanical properties and parametric models showed statistical significance.

In this work, an innovative numerical approach for polylinear approximation (polylinearization) of non-self-intersecting compact sensor characteristics (transfer functions) specified either pointwise or analytically is introduced. The goal is to optimally partition the sensor characteristic, i.e. to select the vertices of the approximating polyline (approximant) along with their positions on, the sensor characteristics so that the distance (i.e. the separation) between the approximant and the characteristic is rendered below a certain problem-specific tolerance. To achieve this goal, two alternative non-linear optimization problems are solved, whose essential difference is in the adopted quantitative measure of the separation between the transfer function and the approximant. In the first problem, which relates to absolutely integrable sensor characteristics (their energy is not necessarily finite, but they can be represented in terms of convergent Fourier series), the polylinearization is constructed by numerical minimization of the L^1--metric (a distance-based separation measure), concerning the number of polyline vertices and their locations. In the second problem which covers the quadratically integrable sensor characteristics (whose energy is finite, but they do not necessarily admit a representation in terms of convergent Fourier series), the polylinearization is constructed by minimizing numerically the L^2-metric (area-, or energy-based separation measure) for the same set of optimization variables –the locations, and the number of polyline vertices.

Background In this study we investigated in detail the role of cannabidiol (CBD), Beta-caryophyllene (BC), or their combinations in diabetic peripheral neuropathy (DN). The key factors that contribute to DN include mitochondrial dysfunction, inflammation, and oxidative stress. Methods Briefly, Streptozotocin (STZ) (55 mg/kg) was injected intraperitoneally to induce DN in Sprague Dawley rats and performed procedures including Randall Sellito Calipers, Von Frey Aesthesiometer, hot plate, and cold plate methods to determine mechanical and thermal hyperalgesia in vivo. The blood flow to the nerves was assessed by using the Laser Doppler device. Schwann cells were exposed to high glucose (HG) at a dose of 30 mM to induce hyperglycemia and DCFDA, JC1 & Mitosox staining were done to determine mitochondrial membrane potential, reactive oxygen species and mitochondrial superoxides in-vitro. The rats were administered i.p with BC (30mg/kg), CBD (15mg/kg), or combination while Schwann cells were treated with 3.65 µM CBD, 75 µM BC, or combination to assess their role in DN amelioration. Results Our results revealed that exposure to BC and CBD diminished HG-induced hyperglycemia in Schwann cells, in part, through reducing mitochondrial membrane potential, reactive oxygen species and mitochondrial superoxides. Further, BC and CBD combination treatment in-vivo could prevent the deterioration of mitochondrial quality control system by promoting autophagy and mitochondrial biogenesis while improving blood flow. CBD and BC treatments also reduced pain hypersensitivity to hyperalgesia and allodynia with increased antioxidant and anti-inflammatory action in diabetic rats. These in vivo effects were attributed to significant upregulation of AMPK, SIRT3, Nrf2, PINK1, PARKIN, LC3B, Beclin1 and TFAM functions while downregulation of NLRP3 inflammasome, NFκB, COX2 and p62 activity was noted as determined by western blotting. Conclusion the present studies demonstrated that STZ & HG induced oxidative and nitrosative stress play a crucial role in the pathogenesis of diabetic neuropathy. We find, for the first time, that CBD and BC combination ameliorate DN via modulating the mitochondrial quality control system.

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

We changed the symmetry of the Weak Force from SU(2) to the quaternion group $Q_8$, and found that spin spacetime separates into two complementary spaces: a spin polarization spacetime of even parity states, and a spin coherence space, in the $S^3$ hypersphere, of odd parity coherent states. Under the quaternion group, spin is a boson of spin 1 in free flight and a fermion of spin $\frac{1}{2}$ when measured. It immediately follows that neutrinos are not needed to balance spin and conserve energy in beta decay. Additionally, we find the boson electrons emitted in beta decay are odd to parity, leading to parity conservation even though the observed beta distribution is asymmetrical.

The main objective of this paper is to introduce a further extension of extended (p, q)-beta function by considering two Mittag-Leffler function in the kernel. We investigate various properties of this newly defined beta function such as integral representations, summation formulas and Mellin transform. We define extended beta distribution and its mean, variance and moment generating function with the help of extension of beta function. Also, we establish an extension of extended (p, q)-hypergeometric and (p, q)-confluent hypergeometric functions by using the extension of beta function. Various properties of newly defined extended hypergeometric and confluent hypergeometric functions such as integral representations, Mellin transformations, differentiation formulas, transformation and summation formulas are investigated.

This study focuses on a new class of functions called sub-b-s-preinvex, that is a generalization of sub-b-s-convex and preinvex functions, and discusses some of their properties. A new sub-b-s-preinvex programming is introduced and the sufficient conditions of optimality under this type of function is established.

The Householder transformation, allowing a rewrite of probabilities into expectations of dichotomic observables, is generalized in terms of its spectral decomposition. Dichotomy is modulated by allowing more than one negative eigenvalues, or by abandoning it altogether, yielding generalized operator valued arguments for contextuality. We also discuss a form of state-dependent contextuality by variation of the functional relations of the operators; in particular, by additivity.

Age is the primary risk factor for neurodegenerative diseases such as Alzheimer’s and Huntington’s disease. Alzheimer’s disease is the most common form of dementia and a leading cause of death in the elderly population of the United States. No effective treatments for these diseases currently exist. Identifying effective treatments for Alzheimer’s, Huntington’s, and other neurodegenerative diseases is a major current focus of national scientific resources, and there is a critical need for novel therapeutic strategies. Here we investigate the potential for targeting the kynurenine pathway metabolite 3-hydroxyanthranilic acid (3HAA) using Caenorhabditis elegans expressing amyloid-beta or a polyglutamine peptide in body wall muscle, modeling proteotoxicity in Alzheimer’s and Huntington’s disease-related, respectively. We show that knocking down the enzyme that degrades 3HAA, 3HAA dioxygenase (HAAO) delays age-associated paralysis in both models. This effect on paralysis was independent of protein aggregation in the polyglutamine model. We also show that the mechanism of protection against proteotoxicity from HAAO knockdown is mimicked by 3HAA supplementation, supporting elevated 3HAA as the mediating event liking HAAO knockdown to delayed paralysis. This work demonstrates potential for 3HAA as a targeted therapeutic in neurodegenerative disease, though the mechanism is yet to be explored.

Cercospora beticola Sacc. is an ascomycete pathogen that causes Cercospora leaf spot in sugar beets (Beta vulgaris L.) and other related crops. The disease symptoms are characterized by circular lesions with an ash-gray centre and dark brown to purple margins on the leaves. It can lead to significant yield losses if not effectively managed. This study aims to characterize and assess the impact of bacterial biological control agents against C. beticola. Following a dual-culture screening, 18 bacteria exhibiting over 50% inhibition were selected, with six of them demonstrating more than 80% control. Identification of the bacteria was carried out through sequencing of the16S rDNA, revealing potentially 12 species belonging to six genera including Bacillus which was represented by four species. Additionally, the bacteria underwent in-depth characterization of biochemical and molecular properties, as well as plant-growth promotion. PCR detection of genes responsible for producing antifungal metabolites revealed that 83%, 78%, 89%, and 56% of the selected bacteria possessed the bacillomycin, iturin, fengycin, and surfactin encoding genes, respectively. Infrared spectroscopy analysis confirmed the presence of lipopeptide structure in the bacteria supernatant filtrate. Subsequently, the bacteria were assessed for their effect on sugar beet plants in controlled conditions. The bacteria exhibited notable capabilities, promoting growth in both roots and shoots, resulting in significant increases in root length, weight, and shoot length. The field experiment with four bacterial candidates demonstrated good performance against C. beticola compared to difenoconazole fungicide. These bacteria played a significant role in disease control, achieving a maximum efficacy of 77.42%, slightly below the 88.51% efficacy attained by difenoconazole. Additional field trials are necessary to verify the protective and growth-promoting effects of these candidates, whether applied individually, combined in consortia, or integrated with chemical inputs in sugar beet crop production.

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.

Fisheries and bottom seawater data were collected in July in 2022 and 2023 from 15 sampling stations in the Huanghe River Estuary and adjacent seas in China. The patterns of functional alpha- and beta-diversity of fish communities in this area and their relationship with environmental factors were studied using trait-based analysis. Five functional classifications, which included 16 functional traits, four functional alpha-diversity indices (functional richness, functional evenness, functional divergence, and community-weighted mean), three functional beta-diversity indices (functional beta-diversity and its turnover and nestedness components), and 14 bottom environmental factors were considered. The dominant traits of fish communities were: benthivorous feeding habits, small and front-facing mouths, high trophic level, demersal, anguilliform, low growth coefficient, medium resilience, low vulnerability, and adapted to warm temperate conditions. The dominant migration traits and types of fish eggs varied by year, and fish abundance was the main factor affecting the dominant traits of the communities. The results of multiple regression on distance matrices and variance partitioning analysis indicated that ammonia nitrogen content, total phosphorus content, and pH were the main environmental factors that affected fish functional diversity. The N/P ratio had an upward control effect on fish functional diversity. Our findings also revealed that high pH gradients and distant geographical distances can inhibit trait turnover in fish communities.

Combining modern thermodynamics theory branches, including finite time thermodynamics or entropy generation minimization, constructal theory and entransy theory, with metallurgical process engineering, this paper provides a new exploration on generalized thermodynamic optimization theory for iron and steel production processes. The theoretical core is to thermodynamically optimize performances of elemental packages, working procedure modules, functional subsystems, and whole process of iron and steel production processes with real finite-resource and/or finite-size constraints with various irreversibilities toward saving energy, decreasing consumption, reducing emission and increasing yield, and to achieve the comprehensive coordination among the material flow, energy flow and environment of the hierarchical process systems. A series of application cases of the theory are reviewed. It can provide a new angle of view for the iron and steel production processes from thermodynamics, and can also provide some guidelines for other process industries.

We report on recent experimental results on β decay into self-conjugate (N=Z) nuclei with mass number 58≤A≤70. Super-allowed β decays from the Jπ=0+ ground state of a Z=N+2 parent nucleus are to the isobaric analogue state, through so-called Fermi transitions, and to Jπ=1+ states, by way of Gamow–Teller (GT) transitions. The operator of the latter decay is a generator of Wigner’s SU(4) algebra and as a consequence GT transitions obey selection rules associated with this symmetry. Since SU(4) is progressively broken with increasing A, mainly as a consequence of the spin–orbit interaction, this symmetry is not relevant for the nuclei considered here. We argue, however, that the pseudo-spin–orbit splitting can be small in nuclei with 58≤A≤70, in which case nuclear states exhibit an approximate pseudo-SU(4) symmetry. To test this conjecture, GT decay strength is calculated with use of a schematic Hamiltonian with pseudo-SU(4) symmetry. Some generic features of the GT β decay due to pseudo-SU(4) symmetry are pointed out. The experimentally observed GT strength indicates a restoration of pseudo-SU(4) symmetry for A=70.

Thalassemia is genetic blood disease cause by absence or decrease of one or more of the globin chain synthesis. Beta thalassemia is characterized by one or more mutations in beta globin gene. Absence or reduced amount the of beta globin chains cause ineffective erythropoiesis which leads to anemia. Beta thalassemia has been further divided into three main forms: Thalassemia minor/silent carrier, major and intermedia. More severe form is thalassemia major in which patients depend upon blood transfusion for survival and high level of iron occur as a consequence of consistent blood transfusion. Over loaded iron invokes the synthesis of reactive oxygen species that are toxic in redundancy and triggering the impairment to vascular, endocrine and hepatic system. Thalassemia can be diagnosed and detected through various laboratory tests such as blood smear, prenatal testing (genetic testing of amniotic fluid), DNA analysis (genetic testing) and complete blood count. Treatment of thalassemia intermedia is symptomatic but it can also be managed by splenectomy and folic supplementation. While thalassemia major can be treated by transplantation of bone marrow, regular transfusion of blood and iron chelation treatment, stimulation of fetal hemoglobin production, hematopoietic stem cell transplantation and gene therapy.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densi- ties and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on dierent set of true values. Some real data sets were employed to show the usefulness and exibility of the model which serves as generalization to many sub-models in the elds of engineering, medical, survival and reliability analysis.

We proposed a so-called Beta Kumaraswamy Burr Type X distribution which gives the extension of the Kumaraswamy-G class of family distribution. Some properties of this proposed model were provided, like: the expansion of densities and quantile function. We considered the Bayes and maximum likelihood methods to estimate the parameters and also simulate the model parameters to validate the methods based on different set of true values. Some real data sets were employed to show the usefulness and flexibility of the model which serves as generalization to many sub-models in the field of engineering, medical, survival and reliability analysis.

A new generalization of extended beta function and its various properties, integral representations and distribution are given in this paper. In addition, we establish the generalization of extended hypergeometric and con uent hypergeometric functions using the newly extended beta function. The properties these extended and con uent hypergeometric functions such as integral representations, Mellin transformations, dif- ferentiation formulas, transformation and summation formulas are also investigated.

With reference to Planck scale, Mach’s relation, increasing support for large scale cosmic anisotropy and preferred directions and by introducing two new parameters Gamma and Beta, right from the beginning of Planck scale, we make an attempt to estimate ordinary matter density ratio, dark matter density ratio, mass, radius, temperature, age and expansion velocity (from and about the baby universe in all directions). We would like suggest that, from the beginning of Planck scale, 1) Dark matter can be considered as a kind of cosmic foam responsible for formation of galaxies. 2) Cosmic angular velocity is directly proportional to squared cosmic temperature. 3) Ratio of critical temperature to actual temperature plays a heuristic role in understanding ordinary and dark matter density ratios. 4) Cosmic expansion velocity increases with decreasing total matter density ratio. 5) There is no need to consider dark energy for understanding cosmic acceleration.

In this paper we introduce the concept of Nano Beta Closure, Nano Beta Interior and study the relationship between them also study some of their properties. Based on these notions we introduced the topological Approach to Decision Making and Its Application in the Medical Field" which describes the use of topological methods in decision-making, specifically through the utilization of nano beta closure and nano beta interior. These mathematical tools are applied in the medical field to improve diagnostic accuracy and aid in treatment planning. The authors demonstrate the effectiveness of this approach through a case study on the diagnosis of Chronic Kidney. The results show that the topological approach using nano beta closure and nano beta interior provides a reliable and accurate method for medical decision-making. Finally, we introduce a medical application for disease groups patients of with chronic kidney. To identify the main causative agent of kidney disease. where using this approach, the medical team can identify the specific areas of the kidney that are affected by the infection, as well as the extent of damage and any potential complications. This information is used to create an individualized treatment strategy that is customized to meet the specific requirements of the patient. and medical history. We write an algorithm that can be a helpful tool for doctors to utilize in diagnosing infection disease Chronic Kidney infections. By utilizing this approach, clinicians can provide accurate diagnoses, develop effective treatment plans, and ultimately improve patient outcomes. finally, we show that fractals hold significant importance in future nano topological generation of the human factor. Their unique properties and self-similar patterns offer insights into the complex organization of biological systems and provide a foundation for designing advanced Nanosystems.

The novel coronavirus pneumonia (COVID-19) is a contagious acute respiratory infectious disease whose causative agent has been demonstrated to be a novel virus of the coronavirus family, SARSCoV-2. A recent pre-print study has showed a heme attack on the 1-beta chain of hemoglobin by COVID19. Beta-thalassemia results of a default in the hemoglobin beta- chain synthesis. 1,5% global population are heterozygotes for this disease. In this study, by a multiple linear regression, we have analyzed the evolution of COVID-19 infection in three Italian regions (Puglia, Sardinia, Sicilia) with different beta-thalassemic prevalences, in order to search a link. The results have showed that betathalassemic heterozygote population prevalence is correlated to immunity against COVID-19, by a regression. This paper is only for academic discussion, the hypotheses and conclusions needs to be confirmed by further research .

Carbapenem antibiotics are the drug of choice for treating multidrug-resistant bacterial infections. Metallo-beta-lactamases (MBLs) are carbapenemase capable of hydrolyzing nearly all therapeutically available beta-lactam antibiotics. Consequently, a need to assess the frequency and phenotypic resistance phenomena of two MBL genes in diarrheal and urinary tract infections (UTIs). Samples were collected through a cross-sectional study, with MBLs genes detected via PCR. Two hundred twenty eight diarrheal bacteria were isolated from 240 samples. The most predominant pathogens were Escherichia coli (32%) and Klebsiella spp. (7%). Phenotypic resistance to amoxicillin-clavulanic acid, aztreonam, cefuroxime, cefixime, cefepime, imipenem, meropenem, gentamicin, netilmicin, and amikacin was 50.4%, 65.6%, 66.8%, 80.5%, 54.4%, 41.6%, 25.7%, 41.2%, 37.2%, and 42.9%, respectively.  Total 142 UTI pathogens were obtained from 150 urine samples, with Klebsiella spp. (39%) and Escherichia coli (24%) are the major pathogens. Phenotypic resistance to amoxycillin-clavulanic acid, aztreonam, cefuroxime, cefixime, cefepime, imipenem, meropenem, gentamicin, netilmicin, and amikacin was 93.7%, 75.0%, 91.5%, 93.7%, 88.0%, 72.5%, 13.6%, 44.4%, 71.1%, and 43%, respectively.  Twenty four diarrheal isolates carried either blaNDM-1 or blaVIM genes; the overall MBL gene prevalence was 10.5%. Thirty six UTI pathogens carried either blaNDM-1 or blaVIM genes (25.4%). Seven isolates carried both blaNDM-1 and blaVIM genes.  MBL genes exhibited a strong association with phenotypic carbapenem and other beta-lactam antibiotic resistance. Resistance to carbapenems requires active surveillance and stewardship.

The stock beta coefficient literature extensively discusses the proper methods for the estimation of beta as well as its use in asset valuation. However, there are relatively few references with respect to the appropriate time horizon that investors should utilize when evaluating the risk-return relationship of a stock. We examine the appropriate time horizon for beta estimation differentiating our results by sector according to the Industry Classification Benchmark. We employ data from the NYSE and we estimate varying lengths of beta employing data from 30 to 250 trading days. The constructed beta series is then examined for the presence of breaks using the endogenous structural break literature. Results show evidence against the use of betas that employ more than 90 trading days of data provisional to the sector under study.

In the present research, we will develop some integral inequalities of Hermite Hadamard type for differentiable η-convex function. Moreover, our results include several new and known results as special cases.

Mutations in KRT1 (keratin 1) or KRT10 (keratin 10) underlie a spectrum of diseases known as keratinopathic ichthyoses. Epidermolytic ichthyosis (EI) is caused by heterozygous missense mutations in the genes KRT1 or KRT10, mutations in the gene KRT2 (keratin 2) lead to superficial epidermolytic ichthyosis, and congenital reticular ichthyosiform erythroderma is caused by frameshift mutations in the genes KRT10 or KRT1, which lead to the phenomenon of revertant mosaicism. Epidermolytic ichthyosis is also present in a mosaic pattern known as epidermolytic (acantholytic) nevus, isolated or diffuse. In the latter case, gonadic involvement is possible, leading to a rare pedigree in which a parent with diffuse epidermolytic nevus (linear EI) gives birth to a child affected by EI. We present here an update on the phenotypic presentations of keratinopathic ichthyoses and their molecular mechanisms.

In this paper, we investigate the generalized Padovan sequences and we deal with, in detail, four special cases, namely, Padovan, Perrin, Padovan-Perrin and modified Padovan sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these sequences. Moreover, we give some identities and matrices related with these sequences.

In this paper, we introduce the generalized Tetranacci quaternions and present some properties of these quaternions.

Asymptotic theories for fractional cointegrations have been extensively studied in the context of time series data, with numerous empirical studies and tests developed. However, most of the previously developed testing procedures for fractional cointegration were primarily designed for time series data. This paper proposes a generalized residual-based test for fractionally cointegrated panels with fixed effects. The test development is based on bivariate panel series with the regressor assumed to be fixed across cross-sectional units. The proposed test procedure accommodates any integration order between [0,1], and it is asymptotically normal under the null hypothesis. Monte Carlo experiments demonstrate that the test exhibits better size and power compared to a similar residual-based test across varying sample sizes.

Vaccination is one of the most effective methods for preventing morbidity and mortality from COVID-19. Vaccine hesitancy has led to a decrease in vaccine uptake; driven by misinformation, fear, and perceptions of vaccine safety. Whole inactivated vaccines have been used in one-fifth of the vaccine recipients in Africa, however there is limited real-world data on their safety. We evaluated the reported side effects and factors associated with reported side effects following vaccination with whole inactivated COVID-19 vaccines - BBiBP-CorV (Sinopharm) and CoronaVac (Sinovac). A quantitative survey evaluating attitudes and side effects from vaccination was administered to 1016 adults presenting at vaccination centers. Two follow-up telephone interviews were conducted to determine side effects after the first and second vaccination dose. Overall, the vaccine was well tolerated; 26.0% and 14.4% reported side effects after the first and second dose respectively. The most frequent local and systemic side effects were pain at the injection site and headaches respectively. Most symptoms were mild, and no participants re-quired hospitalization. Participants who perceived COVID-19 vaccines as safe or had a personal COVID-19 experience were significantly less likely to report side effects. Our findings provide data on the safety and tolerability of whole inactivated COVID-19 vaccines in an African population, providing the necessary data to create effective strategies to increase vaccination and support vaccination campaigns.

Using the method of the beta function, Sun has recently evaluated some series of the type $\sum_{k=0}^{\infty}(ak+b)x^k/\binom{mk}{nk}$. By factorization of the polynomial $t^{m-n}(1-t)^n-x$, we will give a general method to find new $\pi$-series.

This work aims to generate some types of M_(j )–neighborhoods. Relationships among these M_(j )-neighborhoods and some other types of neighborhoods are discussed. Additionally, M_(j )-lower, M_(j )-upper approximations and M_(j )-accuracy in terms of M_(j )-neighborhoods are presented. Their properties, with some examples, are investigated. Finally, We addressed the comparisons among M_(j )approach and other approaches.

Increased activity of transforming growth factor-beta (TGF-β) is a key factor mediating kidney impairment in diabetes. Glomerular podocytes, the crucial component of the renal filter, are a direct target of TGF-β action, resulting in irreversible cell loss and progression of chronic kidney disease (CKD). Urolithin A (UA) is a member of the family of polyphenol metabolites produced by gut microbiota from ellagitannins and ellagic acid-rich foods. The broad spectrum of biological ac-tivities of UA makes it a promising candidate for the treatment of podocyte disorders. In this in vitro study, we investigated whether UA influences the changes exerted in podocytes by TGF-β and high glucose. Following a 7-day incubation in normal (NG, 5.5 mM) or high (HG, 25 mM) glucose the cells were treated with UA and/or TGF-β1 for 24 hours. HG and TGF-β1, each independent and in concert reduced expression of nephrin, increased podocyte motility and up-regulated expression of b3 integrin and fibronectin. These typical for epithelial-to-mesenchymal transition (EMT) effects were inhibited by UA in both HG and NG conditions. UA also reduced the typically elevated in HG expression of TGF-β receptors and activation of TGF-β signal transducer Smad2. Our results indicate that in podocytes cultured in conditions mimicking diabetic milieu, UA inhibits and reverses changes underlying podocytopenia in diabetic kidneys. Hence, UA should be considered as a po-tential therapeutic agent in podocytopathies.

In this study, we aim to evaluate how cyclodextrin molecules affect the hydrophilicity and selec-tivity of PVDF membrane. Herein, we prepared PVDF-PVP(1-x) β-CDx membranes, with x rang-ing from 0 to 1 wt%. The membranes were deeply characterized by means of X-ray diffraction (XRD), attenuated total reflectance infrared (ATR-IR), Raman spectroscopies, Thermal gravimet-ric analysis (TGA), Contact angle measurement (CA), scanning electron microscopy (SEM) and atomic force microscopy (AFM). The study unequivocally demonstrates the effectiveness of the addition of β-CD molecules on membranes' structural, morphological, and dielectric properties. Adding 0.25wt% β-CD enhanced hydrophilicity, with CA decreasing from 72.6° to 56° and roughness decreasing from 81 to 29 nm. The PVDF-PVP(1-x) β-CDx membranes were then fully characterized using electrochemical impedance spectroscopy (EIS) to determine their dielectric properties, which clearly showed that the presence of β-CD induced polarization of the mem-brane. The separation of various dyes with different sizes and charges was utilized. These dyes included methylene blue (MB, positive, 0.504 nm), methyl red (MR, neutral, 0.487 nm), rose Bengal (RB, negative, 0.588 nm), and brilliant blue (BB, negative, 0.798 nm). Based on our re-search, we found that the membrane's selectivity is determined by both exclusion factors (such as size and dielectric properties) and inclusion inside the β-CD cage. We found that using alpha-CD instead of beta-CD led to the disappearance of dye inclusion. These findings strongly sug-gest that β-CD molecules can be a viable solution for dye removal from wastewater.

The classical limit definition of a derivative is expressed in a more general form. The general form includes two arbitrary functions of the parameter for which the limit is calculated. A special case of the general form, which includes scaling and translational symmetry transformations of the limiting parameter, is also discussed. The errors in using the classical definition and the generalized form are calculated for small values of the limiting parameter. The derivatives of some known functions are proven using the new definition. For some well-known functions, a suitable selection of the generalized form may introduce simplicity in calculating the derivatives.

In this paper, it is introduced the notion of r-fuzzy β-T_i, i = 0, 1, 2 separation axioms related to a fuzzy operator β on the initial set X which is a generalization of previous fuzzy separation axioms. An r-fuzzy α-connectedness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of r-fuzzy connectedness. An r-fuzzy α-compactness related to a fuzzy operator α on the set X is introduced which is a generalization of many types of fuzzy compactness.

While vaccines are a well-established method of controlling the spread of infectious diseases, vaccine hesitancy jeopardizes curbing the spread of COVID-19. Through the Vaccine Information Network (VIN), this study explored barriers and motivators to COVID-19 vaccine uptake. We conducted 18 focus group discussions with male and female community members, stratified by country, age group, and—for Zimbabwe only—by HIV status. Participants’ median age across both countries was 40 years (interquartile range of 22–40) and most (65.9%) were female. We conceptualized the key themes within the World Health Organization’s Strategic Advisory Group of Experts on Immunization (SAGE) 3Cs (convenience, confidence, complacency) vaccine hesitancy model. Barriers to vaccine uptake—lack of convenience, low confidence, and high complacency—included inaccessibility of vaccines and vaccination sites, vaccine safety and development concerns, and disbelief in COVID-19’s existence. Motivators to vaccine uptake—convenience, confidence and low complacency—included accessibility of vaccination sites, user-friendly registration processes, trust in governments and vaccines, fear of dying from COVID-19 and knowing someone who had died or become infected with COVID-19. Overall, vaccine hesitancy in South Africa and Zimbabwe was influenced by inconvenience, a lack of confidence, and high complacency around COVID-19 vaccines.

A precise understanding of the genes and associated genomes of SARS-CoV2 is important for various reasons such as discovering origin of the virus and virulence and so on. A thorough descriptive understanding of the SARS-CoV2 genomes and other coronavirus of the beta-coronavirus genus is primarily important. In this article, a set of ten genomes of four CoVs and their associated genes are considered for this present study. A spatial representations of nucleotide bases including purine-pyrimidine representations of the different genes of the corresponding genomes are quantified using Hurst exponent, Shannon entropy and density estimation of different nucleotides including GC content, in order to draw a comparison and contrast among the ten genomes of different types of CoVs which include MERS, SARS-CoV, HKU1 (Human Coronavirus) and associated their genes.

This review was carried out to identify different beta-lactamase resistance genes reported in published literature from Nigeria and to determine the proportion estimates of the important beta-lactamase resistance genes in Nigeria. Sixty-three (63) articles were included in this review based on the eligibility criteria. All the beta-lactamases reported were detected from the Gram-negative bacteria, most especially from Enterobacteriaceae (n=53). Thirty-six different beta-lactamase genes have been reported from Nigeria. These genes belong to the narrow-spectrum, AmpC, extended-spectrum, and carbapenemase beta-lactamase resistance genes. Eight (8) genes (bla_DHA, bla_CTXM-1, bla_CTXM-14, bla_GES-1, bla_VEB-1, bla_OXA-1, bla_OXA-2, and bla_TEM-1) were shared between animals and humans, 5 genes (bla_SHV-1, bla_SHV-2, bla_SHV-11, bla_SHV-12, and bla_NDM-1) were common to both humans and environment while none of the genes was unique to both animals and environment. Four genes including bla_CMY, bla_TEM-1, bla_AmpC, and internationally pandemic bla_CTXM-15 gene were unique to animals, humans, and the environment. No carbapenemase gene was reported from animals yet. The pooled proportion estimate of ESBL genes in Nigeria was 31% (95% CI: 26-36%, P<0.0001), while the estimate of bla_CTXM-15 gene in Nigeria was 46% (95% CI: 36-57%, P<0.0001). The proportion estimate of AmpC genes was 32% (95% CI: 11-52%, P<0.001), while the estimate for carbapenemases was 8% (95% CI: 5-12%, P<0.001). This study has provided information on the beta-lactamases distribution in Nigeria. This is necessary for a better understanding of molecular epidemiology of clinically important beta-lactamases especially the extended-spectrum beta-lactamases and carbapenemases in Nigeria.

Behavior analysis is a widely used non-invasive tool in the practical production routine, as the animal acts as a biosensor capable of reflecting its degree of adaptation and discomfort to some environmental challenge. Predominantly, conventional statistics use occurrence data for behavioral evaluation and well-being estimation, disregarding the temporal sequence of events. The Generalized Sequential Pattern (GSP) algorithm is a data mining method that identifies recurrent sequences that exceed a user-specified support threshold, whose potential has not yet been investigated for broiler chickens in enriched environments. Enrichment aims to increase environmental complexity with promising effects on animal welfare, stimulating priority behaviors and potentially reducing the deleterious effects of heat stress. The objective was to validate the application of the GSP algorithm to identify temporal correlations between heat stress and the behavior of broiler chickens in enriched environments through proof of concept. Video image collection was carried out automatically for 48 continuous hours, analyzing a continuous period of seven hours, from 12:00 PM to 6:00 PM, during two consecutive days of tests for chickens housed in enriched and non-enriched environments under comfort and stress temperatures. Chickens at comfort temperature showed high motivation to perform the behaviors of Preening (P), Foraging (F), Lying down (Ld), Eating (E), and Walking (W) whose sequences &lt;{Ld,P}&gt;; &lt;{Ld,F}&gt;; &lt;{P,F,P}&gt;; &lt;{Ld,P,F}&gt; and &lt;{E,W,F}&gt; were the only ones observed in both treatments. All other sequential patterns (comfort and stress) were distinct, suggesting that environmental enrichment alters the behavioral pattern of broiler chickens. Heat stress drastically reduced the sequential patterns found at the 20% threshold level in the tested environments. The behavior of lying laterally "Ll" is a strong indicator of heat stress in broilers and was only frequent in the non-enriched environment, which may suggest that environmental enrichment provides the animal with better opportunities to adapt to stress-inducing challenges, such as heat.

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum spacetime. It is based in the Minimum Group Representation Principle (MGRP). Within this framework new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space-times. Our main results here are: {\bf(i)} We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, as the spectral scalar and tensor indices, $n_S$ an $n_T$, and the tensor to scalar ratio $r$. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. {\bf(ii)} The pure entangled states in the minimum group (metaplectic) $Mp(n)$ representation for quantum de Sitter space-time and black holes are found. {\bf(iii)} For entanglement, the relation between the Schmidt type representation and the physical states of the $Mp(n)$ group is found: This is a {\it new non-diagonal} coherent state representation complementary to the known Sudarshan diagonal one. {\bf(iv)} Mean value generators of $Mp(2)$ are related to the adiabatic invariant and topological charge of the spacetime (matrix element of the transition $-\infty < t < \infty$). {\bf(v)} The basic {\it even} and {\it odd} $n$-sectors of the Hilbert space are intrinsic to the quantum spacetime and its discrete levels (in particular continuum for $n \rightarrow \infty$), they do not require any extrinsic generation process as the standard Schrodinger cat states, and are {\it entangled}. {\bf(vi)} The gravity or cosmological domains in one side and another of the Planck scale are {\it entangled}. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity reqion and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space-time are entangled. {\bf(vii)} The general classical-quantum gravity duality is associated to the Metaplectic $Mp(n)$ group symmetry which provides the complete full covering of the phase space and of the quantum space-time mapped from it.

Background: Periodontitis is a disease that leads to serious functional and aesthetic dysfunctions resulting in impairment of life quality; it exists in different forms and its etiology is related with multiple component causes. Angiogenesis, together with inflammatory infiltrate, are two key processes in the evolution of inflammatory processes involving gingival tissues. The aim of this study was to evaluate their alterations in relation to some important periodontal diseases-associated factors (i.e. smoke, sex, age, plaque, pus, probing pocket depth) in patients with diagnosis of Generalized Aggressive Periodontitis (GAP). Methods: Eighteen subjects with GAP were enrolled for this study. Percentage of inflammatory cells and vascular area were measured and evaluated in relation with each periodontal diseases-associated factor. Results: The results showed a significant decrease of the percentage of vascular area in association with almost all the periodontal diseases-related factors (smoke, age, PPD, plaque) and not significant differences in the percentage of inflammatory cells. Conclusions: Data suggest that, even if these factors are often commonly related to worsening of periodontal status, they did not affect inflammatory and vascular pattern, as we can assume. For the future, additional studies, aimed to evaluated each singular factor in a wider sample size, should be planned.

Studies on crop response to light quality [red (R) to far-red (FR) light ratio] often recommend early weed removal to reduce the effects of shade avoidance responses on crop yield. However, it is unclear whether crops are able to distinguish reflected light quality of kin from that of non-kin. We evaluated the response of sugarbeet (Beta vulgaris L.) to reflected FR light from sugarbeet, common lambsquarters (Chenopodium album L.), Kentucky bluegrass (Poa pratensis L.), alfalfa (Medicago sativa L.), and bare soil (control) under outdoor conditions in 2016 and 2017. Treatments were completely randomized with 10 replications per treatment. The study methods ensured there was no direct resource competition. The reflected R:FR of plant species ranged from 0.06 (common lambsquarters) to 0.24 (sugarbeet) compared to 0.7 for the bare soil. In both 2016 and 2017, there were 2 to 4 more leaves in the sugarbeet surrounded by soil compared to sugarbeet surrounded by neighboring species. There was up to 47, 57, 43, and 23% reduction in sugarbeet leaf area, shoot dry weight, root diameter, and root dry weight, respectively, due to reflected R:FR light from neighboring species. Sugarbeet did not respond differently to reflected light quality of kin compared to non-kin.

We introduce a new generalized inverse (i.e., generalized EP element) which is a natural generalization of EP and *-DMP elements in a Banach *-algebra. We present polar-like characterizations of generalized EP elements. The necessary and sufficient conditions under which the sum of two generalized EP elements is a generalized EP element are investigated. Finally, the generalized core-EP orders for generalized EP elements are characterized.

One open question remains regarding the theory of the generalized variational principle, that is, why the stress-strain relation still be derived from the generalized variational principle while the Lagrangian multiplier method is applied in vain? This study shows that the generalized variational principle can only be understood and implemented correctly within the framework of thermodynamics. As long as the functional has one of the combination $A(\epsilon_{ij})-\sigma_{ij}\epsilon_{ij}$ or $B(\sigma_{ij})-\sigma_{ij}\epsilon_{ij}$, its corresponding variational principle will produce the stress-strain relation without the need to introduce extra constraints by the Lagrangian multiplier method. It is proved herein that the Hu-Washizu functional $\Pi_{HW}[u_i,\epsilon_{ij},\sigma_{ij}]$ and Hu-Washizu variational principle comprise a real three-field functional.

In this paper, we introduce the generalized dual hyperbolic Fibonacci numbers. As special cases, we deal with dual hyperbolic Fibonacci and dual hyperbolic Lucas numbers. We present Binet's formulas, generating functions and the summation formulas for these numbers. Moreover, we give Catalan's, Cassini's, d'Ocagne's, Gelin-Cesàro's, Melham's identities and present matrices related with these sequences.

The main objective of this paper is to introduce k-fractional derivative operator by using the definition of k-beta function. We establish some results related to the newly defined fractional operator such as Mellin transform and relations to k-hypergeometric and k-Appell's functions. Also, we investigate the k-fractional derivative of k-Mittag-Leffler and Wright hypergeometric functions.

Crustacean hyaluronidases are 1 poorly understood both in terms of their enzymatic properties and in terms of their structural features. In this work, we have shown that the hepatopancreas homogenate of the red king crab has a hyaluronidase activity that is an order of magnitude higher than its commercial counterpart. Zymography revealed the hyaluronidase activity of the protein roughly from40 to 50 kDa relative to the molecular marker used in electrophoresis. Analysis of the hepatopancreas transcriptome revealed a hyaluronidase sequence with an expected molecular weight of 42.5 kDa. It turned out that the reaction of cleavage of hyaluronate in the presence of a homogenate proceeds by the mechanism of b-elimination, which is well known for bacterial hyaluronidases. Thus, a new hyaluronidase of higher eukaryotes was found and described, which is not integrated into the modern classification of hyaluronidases.

It is shown that the 5D geodetic equations and 5D Ricci identities give us a way to create a new viewpoint on some problems of Modern Physics, Astrophysics, and Cosmology. Specifically, the application of the 5D geodetic equations in (4+1) and (3+1+1) splintered forms obtained with the help of the monad and dyad methods made it possible to introduce a new, effective generalized concept of the rest mass of the elementary particle. The latter leads one to novel connections between the General Relativity and quantum field theories, as well as all of that, including the (4+1) splitting of the 5D Ricci identities, brings about a better understanding of the magnetic monopole problem and the vital difference in the origins of the Maxwell equations and gives rise to surprising connections between them. The obtained results also provide new insight into the mechanism of the 4D Universe’s expansion and its following acceleration.

We study the generalized χ and η cross helicities for non-ideal non-barotropic magnetohydrodynamics (MHD). χ and η, the additional label translation symmetry group, have been used to generalize the cross helicity in ideal flows. Both new helicities are additional topological invariants of ideal MHD. To study there behaviour in non-ideal MHD, we derive the time derivative of both helicities using the non-ideal MHD equations taking viscosity, finite resistivity and heat conduction into account. Physical variables are divided into ideal and non-ideal quantities separately during the mathematical analysis for simplification. The analytical results indicate that χ and η cross helicities are not strict constant of motion in the non-ideal MHD and show the rate of dissipation which is compared to the dissipation of other topological constants of motion.

In the paper, the authors find two explicit formulas and recover a recursive formula for the generalized Motzkin numbers. Consequently, the authors deduce two explicit formulas and a recursive formula for the Motzkin numbers, the Catalan numbers, and the restricted hexagonal numbers respectively.

Introduction: This study aims to elucidate the clinical diagnostic value of S100 Calcium Binding Protein beta (S100B) in epilepsy, a topic of ongoing debate among European and Asian epilepsy research centres.Methods and analysis: A structured long-term research plan was developed, comprising three phases. Phase one involves observational studies investigating the correlation between S100B levels in serum or cerebrospinal fluid and epilepsy. Phase two integrates observational and randomised controlled data to establish baseline S100B levels across diverse epilepsy demographics, underpinning the predictive value of S100B for epilepsy. Phase three focuses on randomised controlled trials to evaluate the diagnostic accuracy of S100B as an epilepsy biomarker.Ethics and dissemination: All enrolled patients will provide written consent. The ethics committee of the Second People’s Hospital of Gansu Province, Affiliated Hospital of Northwest Minzu University, China, approved the study (GSSEY2022-KY009-01).Registration: The study is registered with PROSPERO (CRD42023425431).

Bergamot flavonoids have been shown to prevent metabolic syndrome, non-alcoholic fatty liver disease (NAFLD) and stimulate autophagy in animal models and patients. To investigate further the mechanism of polyphenol-dependent effects, we performed RT2-PCR array analysis on 168 metabolism, transport and autophagy-related genes expressed in rat livers exposed for 14 weeks to different diets: standard, cafeteria (CAF) and CAF diet supplemented with 50 mg/kg of Bergamot Polyphenol Fraction (BPF). CAF diet caused a strong upregulation of the gluconeogenesis pathway (Gck, Pck2) and a moderate (>1.7 fold) induction of genes regulating lipogenesis (Srebf1, Pparg, Xbp1), lipid and cholesterol transport or lipolysis (Fabp3, Apoa1, Lpl) and inflammation (Il6). However, only one -oxidation gene (Cpt1a) and a few autophagy genes were modulated in the CAF group compared to controls. While most of these transcripts were significantly modulated by BPF, we observed a particularly potent effect on lipogenesis genes, like Acly, Acaca, Fasn and Scd1, which were suppressed far below the mRNA levels of control livers as confirmed by alternative primers-based RT2-PCR analysis and western blotting. These effects were accompanied by downregulation of pro-inflammatory cytokines (Il6, Tnfa, and Il10) and diabetes-related genes. Few autophagy (Map1Lc3a, Dapk) and no -oxidation gene expression changes were observed, suggesting minor transcriptional effects on autophagy. In conclusion, chronic BPF supplementation efficiently prevents NAFLD by modulating hepatic energy metabolism and inflammation gene expression programs, with no effect on -oxidation, but profound suppression of de-novo lipogenesis.

(1) Background: Angiotensin II, a major culprit in cardiovascular disease, activates mediators that are also involved in pathological cardiac remodelling. We aimed at investigating the effects of two of them: aldosterone (Ald) and transforming growth factor-beta-1 (TGF-β1 ), on cardiac remodelling in an in vivo model. (2) Methods: Six-week-old male wild-type (WT) and TGF-β1 -overexpressing transgenic (TGF-β1 -TG) mice were infused with subhypertensive doses of Ald for 2 weeks, and/or treated orally with eplerenone from postnatal day 21. Heart’s ventricles were examined: by morphometry, immunoblotting to assess intracellular signalling pathways, RT qPCR to determine hypertrophy and fibrosis marker genes. (3) Results: TGF-β1 -TG mice spontaneously developed cardiac hypertrophy and interstitial fibrosis, exhibited higher baseline phosphorylation of p44/42 and p38 kinases, fibronectin and ANP mRNA expression. Ald induced a comparable increase in ventricular heart weight-to-body-weight ratio and cardiomyocyte diameter in both strains, but less pronounced increase in interstitial fibrosis in transgenic compared to WT mice (23.6% vs 80.9%, p&lt;0.005). Ald increased phosphorylation of p44/42 and p38 in WT but not TGF-β1 -TG mice. While eplerenone-enriched chow partially prevented Ald-induced cardiac hypertrophy in both genotypes and interstitial fibrosis in WT controls, it completely protected from additional fibrosis in transgenic mice. (4) Conclusions: Ald appears to induce cardiac hypertrophy independently of TGF-β1 , while in case of fibrosis downstream signalling pathways of these two factors probably converge

Pancreatic beta cells secrete insulin in response to stimulation with glucose and other nutrients, and impaired insulin secretion plays a central role in development of diabetes mellitus. Pharmacological management of diabetes includes various antidiabetic drugs, including incretins. The incretin hormones, glucagon-like peptide-1 and gastric inhibitory polypeptide, potentiate glucose-stimulated insulin secretion by binding to G protein-coupled receptors, resulting in stimulation of adenylate cyclase and production of the secondary messenger cAMP, which exerts its intracellular effects through activation of protein kinase A or the guanine nucleotide exchange protein 2A. The mo-lecular mechanisms behind these two downstream signaling arms are still not fully elucidated and involve many steps in the stimulus-secretion coupling cascade, ranging from the proximal regula-tion of ion channel activity, to the central Ca2+ signal, and the most distal exocytosis. In addition to modifying intracellular coupling, the effect of cAMP on insulin secretion could also be at least partly explained by the impact on intercellular coupling. In this review, we systematically describe the possible roles of cAMP at these intra- and inter-cellular signaling nodes, keeping in mind the rele-vance for the whole organism and translation to humans.

Iloperidone (ILO) is a second-generation antipsychotic drug and a first-line treatment approved by USFDA in May 2009. Iloperidone belongs to Biopharmaceutical Classification Systems (BCS) class II; thus, it is poorly water-soluble, highly permeable, and has pH-dependent solubility. Cyclodextrins and their derivatives have a wide range of applications in different formulations due to their complexation ability, which improves the solubility, stability, safety, and bioavailability of a drug. We have tried the complexation of iloperidone with sulfobutyl ether-β-cyclodextrin (SEβCD) to improve its solubility and dissolution. Complexation was done by the kneading method. The characterization of the SEβCD complexes with Iloperidone was done by FTIR, differential scanning calorimetry (DSC), saturation solubility, etc. A multimedia dissolution of the complex was carried out and compared with the plain drug. A significant improvement in drug release was found from SEβCD complexes in all media when compared with the drug alone.

Background: The antimalarial drug chloroquine and antimicrobial drug azithromycin have received significant attention during the current COVID-19 pandemic. Both drugs can alter cardiac electrophysiology and have been associated with drug-induced arrhythmias. Meanwhile, sympathetic activation is commonly observed during systemic inflammation and oxidative stress (e.g., in SARS-CoV-2 infection), and may influence the electrophysiological effects of chloroquine and azithromycin. Here, we investigated the effect of beta-adrenergic stimulation on proarrhythmic properties of chloroquine and azithromycin using a detailed in silico model of ventricular electrophysiology. Methods: Concentration-dependent chloroquine and azithromycin-induced alterations in ion-channel function were incorporated into the Heijman canine ventricular cardiomyocyte model. Single and combined drug effects on action-potential (AP) properties were analyzed using a population of 592 models accommodating inter-individual variability. Sympathetic stimulation was simulated by an increase in pacing rate and experimentally validated isoproterenol-induced changes in ion-channel function. Results: At 1 Hz pacing, therapeutic doses of chloroquine and azithromycin (5 and 20 µM, respectively) individually prolonged AP duration (APD) by 33% and 13%. Their combination produced synergistic APD prolongation (+161%) with incidence of proarrhythmic early afterdepolarizations in 53.5% of models. Increasing the pacing frequency to 2 Hz shortened APD and together with 1 µM isoproterenol corrected the drug-induced APD prolongation. No afterdepolarizations occurred following increased rate and simulated application of 0.1-1 µM isoproterenol. Conclusion: Sympathetic stimulation limits chloroquine- and azithromycin-induced proarrhythmia by reducing their APD-prolonging effect, suggesting the importance of heart rate and autonomic status monitoring in particular conditions (e.g., COVID-19).

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

In this paper, we introduce the notion of weighted generalized group inverse in a Banach algebra with proper involution. This is a natural generalization of weighted weak group inverse for a complex matrix and Hilbert space operator. We present several characterizations and representations of this generalized inverse. In addition, a new partial order on elements in a Banach *-algebra is investigated by using the weighted generalized group inverse and some known results are thus generalized.

Let {ξ1, ξ2. . . .} be a sequence of independent possibly differently distributed random variables defined on a probability space (Ω, F, P) with distribution functions {F_ξ1., F_ξ2 , . . .}. Let η be a counting random variable independent of sequence {ξ1, ξ2. . . .}. In this paper, we find conditions under which distribution function of randomly stopped sum Sη = ξ1 + ξ2 + . . . + ξη belongs to the class of generalized subexponential distributions.

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of the generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss generating function approach using which we derive different entropy measures. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

The neutrino is perhaps the most elusive member of the particle zoo. The questions about its nature, namely: Dirac or Majorana, the value of its mass and the interactions with other particles, the number of its components including sterile species, are long standing ones and still re- main in large extent without conclusive answers. From the side of the nuclear structure and nuclear reactions, both theories and experiments, the need to elucidate these questions have, and still has, prompt crucial developments in the fields of double beta decay, double charge exchange and neutrino induced reactions. The measurements of neutrino flavor os- cillation parameters contribute largely to restrict models with massless neutrinos. From the particle physics side, the possibilities to extent the standard model of electroweak interactions to incorporate a right handed sector of the electroweak lagrangian are directly linked to the adopted neu- trino model. Here, I would like to address another aspect of the problem by asking the question of the neutrino mass mechanism in the cosmological context, and particularly about dark matter.

Searching for neutrinoless double beta decay is a top priority in particle and astroparticle physics, being the most sensitive test of lepton number violation and the only suitable process to probe the Majorana nature of neutrinos. In order to increase the experimental sensitivity for this particular search, ton-scale detectors operated at nearly zero-background conditions with a few keV energy resolution are required. In this scenario, cryogenic detectors have proven effective in addressing many of these issues simultaneously. After long technical developments, the CUORE experiment established the possibility to operate large scale detectors based on this technology. Parallel studies pointed out that scintillating cryogenic detectors represent a suitable upgrade for the CUORE design, directed towards higher sensitivities. In this work, we review the recent development of cryogenic detectors, starting from the status of the art and outlying the path toward next-generation experiments.

Diabetes mellitus (DM) is one of the most prevalent metabolic disorders. In order to replace the function of the destroyed pancreatic beta cells in diabetes, islet transplantation is the widely practiced treatment; however, it has several limitations. As an alternative approach, human pluripotent stem cells (hPSCs) can provide an unlimited source of pancreatic cells that have the ability to secrete insulin in response to high blood glucose level. However, determination of the appropriate pancreatic lineage candidate for the purpose of cell therapy for treatment of diabetes is still debated upon. While hPSC-derived beta cells are perceived as the ultimate candidate, the efficiency needs further improvement in order to obtain a sufficient number of glucose responsive β-cells for transplantation therapy. On the other hand, hPSC-derived pancreatic progenitors can be efficiently generated in vitro and can further mature into glucose responsive beta cells in vivo after transplantation. Herein, we discuss the advantages and predicted challenges associated with the use of each of the two pancreatic lineage products for diabetes cell therapy. Furthermore, we address co-generation of functionally relevant islet cell subpopulations and structural properties contributing to glucose responsiveness of beta cells, as well as the available encapsulation technology for these cells.

Alveolar Rhabdomyosarcoma (ARMS), an invasive subtype of Rhabdomyosarcoma (RMS), is associated with chromosomal translocation events resulting in one of two oncogenic fusion genes PAX3-FOXO1 or PAX7-FOXO1. ARMS patients exhibit an overexpression of the pleiotropic cytokine Transforming growth factor beta (TGF-β). This overexpression of TGF-β1 causes an increased expression of a downstream transcription factor called SNAIL, which promotes Epithelial to Mesenchymal Transition (EMT). Overexpression of TGF-β also inhibits myogenic differentiation, making ARMS patients highly resistant to chemotherapy. In this review, we first describe different types of RMS and then focus on ARMS and the impact of TGF-β in this tumor type. We next highlight current chemotherapy strategies including a combination of FDA approved drugs vincristine, actinomycin D, and cyclophosphamide (VAC), Cabozantinib, Bortezomib, Vinorelbine, AZD 1775 and cisplatin. Lastly, we discuss chemotherapy agents that target the differentiation of tumor cells in ARMS which include all trans retinoic acid (ATRA) and 5-Azacytidine. Improving our understanding of the role of signaling pathways, such as TGF-β1, in the development of ARMS tumor cells differentiation will help inform more tailored drug administration in the future.

There is clinical concern about the combined use of alcohol and opiates. Several lines of evidence support an interaction between alcohol and the endogenous opioid system. Thus, we hypothesized that ethanol by causing the release of opioid peptides may sensitize the system to the action of exogenous opioids such as morphine. In this study, using the place conditioning paradigm as an animal model of reward, we determined whether a morphine challenge would alter the pre-established preference induced by ethanol conditioning in mice, and whether this response was mediated by the mu opioid receptor (MOP). Given that ethanol exposure stimulates the release of opioid peptides, we also assessed the role of beta-endorphin (β-END) and enkephalins (ENKs) in this response. Mice lacking MOP, β-END and/ or ENKs as well as their respective wild-type controls were tested for baseline place preference on day 1, conditioned with ethanol (2 g/kg) versus saline on days 2 to 4 and then tested under a drug-free state for postconditioning place preference on day 5. On day 8, mice received a single injection of morphine (5 mg/kg) and were tested for place preference. On each test day, mice were placed in the central neutral chamber and allowed to freely explore the conditioning chambers. The amount of time that mice spent in each chamber was recorded. We found that a challenge dose of morphine given on day 8 enhanced the CPP response in mice previously conditioned with ethanol. This response was abolished in MOP null mice, confirming the role of MOP in this response. Although this enhanced response was not altered in mice lacking either β-end or ENKs compared to their wild-type littermates/controls, it was completely blunted in mice lacking both β-end and enkephalins. Together, these results suggest that these opioid peptides jointly mediate the crosstalk between the rewarding actions of morphine and ethanol.

The response of plasmonic metal particles to an electromagnetic wave undergoes significant features at the nanoscale level. Different properties of the internal composition of a metal, such as its ionic background and the free electron gas, begin to manifest more prominently. As the dimensions of the nanostructures decrease, the classical local theory gradually becomes inadequate. Therefore, Maxwellʹs equations need to be supplemented with a relationship determining the dynamics of current density which is the essence of nonlocal plasmonic models. In this field of physics, the standard (linearized) hydrodynamic model (HDM) has been widely adopted with great success, serving as the basis for a variety of simulation methods. However, ongoing efforts are also being made to expand and refine it. Recently, the GNOR (general nonlocal optical response) modification of the HDM has been used, with the intention of incorporating the influence of electron gas diffusion. Clearly, from the classical description of fluid dynamics, a close relationship between viscosive damping and diffusion arises. This offers a relevant motivation for introducing the GNOR modification in an alternative manner. The standard HDM and its existing GNOR modification also do not include the influence of interband electron transitions in the conduction band and other phenomena that are part of many refining modifications of the Drude‐Lorentz and other models of metal permittivity. In this article, we present a modified version of GNOR‐HDM that incorporates the viscosive damping of the electron gas and a generalized Drude‐Lorentz term. In the selected simulations, we also introduce Landau damping which corrects the magnitude of the standard damping constant of the electron gas based on the size of the nanoparticle. We have chosen a spherical particle as a suitable object for testing and comparing HD models and their modifications because it allows finding precise analytical solutions for the interaction and, simultaneously, it is a relatively easily fabricable nanostructure in practice. Our contribution also includes our own analytical method for solving the HDM interaction of a plane wave with a spherical particle. This method forms the core of calculations of the characteristic quantities, such as the extinction cross‐sections and the corresponding components of electric fields and current densities.

Two extensions of the generalized double Lomax distribution are introduced - the spliced-scale generalized double Lomax distribution and the exponentiated generalized double Lomax distribution. Their properties are studied. Usefulness of the new distributions is shown by fitting them to stock returns datasets.

In this paper we investigate the geometric structure and control of exponential families depending on additional parameters, called external parameters. These generalized exponential families emerges naturally when one applies the maximum entropy formalism to derive the equilibrium statistical mechanics framework. We study the associated statistical model, compute the Fisher metric and introduce a natural fibration of the parameter space over the external parameter space. The Fisher Riemannian metric allows to endow this fibration with an Ehresmann connection and to study the geometry and control of these statistical models. As an example, we show that horizontal lift of paths in the external parameter space corresponds to an isentropic evolution of the system. We apply the theory to the example of a ideal gas in a rotating rigid container. Most of the results are expressed in local coordinates; in the appendices we hint at possible global extensions of the theory.

Abstract: Due to their rapid evolution and their impact on health care, be-ta-lactamases, protein degrading beta-lactam antibiotics, are used as generic model of protein evolution. Therefore, we investigated the mutation effects in two distant beta-lactamases TEM-1 and CTX-M-15. Interestingly we found a site with a complex pattern of genetic interactions. Mutation G251W in TEM-1 is in-activating the protein’s function just as the reciprocal mutation W251G in CTXM-15. Phylogenetic analysis revealed that mutation G has been entrenched in TEM-1 background: while rarely observed throughout the phylogeny it is es-sential in TEM-1. Using a rescue experiment in TEM-1 G251W mutant, we could identify sites that alleviates the deviation from G to W. While few of these muta-tions could potentially involve local interactions, most of them were found on distant residues in the 3D structure. Many well-known mutations having an impact on protein stability, such as M182T, were recovered. Our results there-fore suggest that entrenchment of an amino acid may rely on diffuse interactions among multiple sites with a major impact on protein stability.

Wnt/β-catenin signaling pathway plays an established role in various diseases and is considered a hallmark of endometrial cancer (EC). Special AT-rich sequence-binding protein 1 and 2 (SATB1 and SATB2) are nuclear matrix-associated proteins involved in chromatin remodeling and regulation of gene expression. SATB1 promotes the progression of numerous types of cancers, whereas SATB2 acts as a tumor suppressor. Despite a recent progress in our knowledge about EC, the exact mechanisms that control their proliferation and metastatic potential still remain unknown. The aim of our study was to investigate the association between Wnt3A, β-catenin, SATB1 and SATB2 protein level and the clinicopathological features of EC patients. 92 EC patients, aged 37-84, were enrolled to our study. The immunoexpression of WNT3A was found in specimens from all EC patients, β-catenin was expressed in 97% of the cases, SATB1 in 87%. The significant association between Wnt3a expression and tumor grade was found; moreover mean IRS for Wnt3a turned out to be significantly lower in high-grade tumors than in low-grade malignancies (p=0.038). In turn, immunoexpression of β-catenin varied significantly across FIGO stages and was associated with the presence of lymph node metastases. Mean IRS for β-catenin in patients with lymph node metastases was significantly lower than in those without (p = 0.028). The Kaplan-Meier analyses demonstrated a stepwise impairment of cancer overall survival with increasing SATB1 expression. In conclusion, both Wnt/β-catenin signaling pathway and SATB1 contribute to progression of EC. Downregulation of β-catenin may predispose to lymphatic spread of EC. In turn, downregulation of Wnt3a seems to be characteristic for high-grade tumors, but probably does not play a role in formation of lymph node metastases. The important role of SATB1 as a predictor of poor survival and could be helpful in establishing a more accurate prognosis in endometrial cancer patients.

We recently reported that in the spinal cord of PPMS or SPMS patients, large areas of periplaque demyelinating lesions extend distance away from plaque borders. Such lesions are characterized by a progliotic TGF-beta 1 signature accompanied by: i) a low-grade inflammatory reaction, ii) an extensive astrocytosis and iii) a process of incomplete demyelination. It was proposed that, while efficiently dampening inflammation in MS spinal cords, TGF-beta 1 could promote astrocytosis, prevent remyelination and possibly trigger alterations of myelin synthesis. In light of these findings, a re-interpretation of two large neuropathological studies performed on MS brains and spinal cords is provided here. While results from these studies clearly showed that active plaques do not display any region-specific distribution, an important point was apparently overlooked and not discussed by the authors: a significantly higher percentage of inactive plaques was found in MS spinal cords as compared to brains and, conversely, the percentage of slowly-expanding (or smoldering) lesions was significantly lower in the spinal cord as compared to the brain. These data indicate that the spinal cord environment may be more favorable to the resolution of inflammation. Downstream of the autoimmune process leading to plaque formation, region-specific mechanisms may thus drive the outcome of active plaques. While inflammation triggers tissue destruction, inflammation may also be needed for effective tissue repair and an inappropriate dampening of inflammatory events may possibly translate into a poor level of remyelination in MS spinal cords. It is proposed here that TGF-beta 1 is involved in such a brain-spinal cord dissociation of active plaques outcome.

This paper focuses on establishing boundedness properties and Parseval-Goldstein type relations for the generalized Mehler-Fock transform initially introduced by B. L. J. Braaksma and B. M. Meulenbeld (Compositio Math.,{18}(3):235-287, 1967. Also, we derive an inversion formula for this transform over Lebesgue spaces.

Uchino first initiated the study of generalized Reynolds operators on associative algebras. Recently, related research has become a hot topic. In this paper, we first introduce the notion of generalized Reynolds operators on Hom-Lie triple systems associated to a representation and a 3-cocycle. Then, we develop cohomology of generalized Reynolds operators on Hom-Lie triple systems with coefficients in a suitable representation. As applications, we use the first cohomology group to classify linear deformations and we study the obstruction class of an extendable order $n$ deformation. Finally, we introduce and investigate Hom-NS-Lie triple system as the underlying structure of generalized Reynolds operators on Hom-Lie triple systems.

Throughout this paper, we will establish a comprehensive theoretical foundation and rigorously develop the methodology to investigate the structure of quotient ring S/P under the influence of symmetric generalized n-derivations, where S represents an arbitrary ring, and P signifies a prime ideal of S satisfying certain algebraic identities acting on prime ideal P without relying on the assumption of primeness or semi-primeness of the ring.

In this article we investigate the generalized Kawahara-KdV system. A new topological approach is applied to prove the existence of at least one classical solution and at least two nonnegative classical solutions. The arguments are based upon recent theoretical results.

In this paper, we mainly show that generalized hyperharmonic number sums with reciprocal binomial coefficients can be expressed in terms of classical (alternating) Euler sums, zeta values and generalized (alternating) harmonic numbers.

In this paper, we investigate the recurrence properties of the generalized Tribonacci sequence and present how the generalized Tribonacci sequence at negative indices can be expressed by the sequence itself at positive indices.

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.

Based on previous research results, we propose a new preprocessing HSS iteration method (PHSS) for the generalized Lyapunov equation. At the same time, the corresponding inexact PHSS algorithm (IPHSS) is given from the angle of application. All the new methods presented in this paper have given the corresponding convergence proof. The numerical experiments are carried out to compare the new method with the existing methods, and the improvement effect is obvious. The feasibility and effectiveness of the proposed method are proved from two aspects of theory and calculation.

This study investigates the metabolic parallels between stimulated pancreatic beta cells and cancer cells, emphasizing glucose and glutamine metabolism. Addressing the significant public health challenges of Type 2 Diabetes Mellitus (T2DM) and cancer, we aim to deepen understanding of the mechanisms driving insulin secretion and cellular proliferation. Our analysis of anaplerotic cycles and NADPH's role in biosynthesis elucidates their vital functions in both processes. Additionally, we find that both cell types share an antioxidative response mediated by the Nrf2 signaling pathway, glutathione synthesis, and UCP2 upregulation. Notably, UCP2 facilitates the transfer of C4 metabolites, enhancing reductive TCA cycle metabolism. We also uncover that hypoxic responses are transient in beta cells post-stimulation but persistent in cancer cells. By synthesizing these insights, our research suggests novel therapeutic targets for T2DM, highlighting the shared metabolic strategies of stimulated beta cells and cancer cells. This comparative analysis not only illuminates the metabolic complexity of these conditions but also emphasizes the crucial role of metabolic pathways in cell function and survival, offering fresh perspectives for tackling T2DM and cancer challenges.

We establish a new Gagliardo-Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behaviour. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with Hs-subcritical nonlinearities, either of local or non-local nature.

The prim objective of commenced article is to determine q-sumudu transforms of a product of unified family of q-polynomials with basic (or q-) analogue of fox’s H-function and q-analog of I-functions. Specialized cases of the leading outcome are further evaluated as q-sumudu transform of general class of q-polynomials and q-sumudu transforms of the basic analogues of Fox’s H-function and I-functions.

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.

Prebiotic dietary fiber supplements are commonly consumed to help meet fiber recommendations and improve gastrointestinal health by stimulating beneficial bacteria and the production of short-chain fatty acids (SCFAs), molecules beneficial to host health. The objective of this research project was to compare potential prebiotic effects and fermentability of five commonly consumed fibers using an in vitro fermentation system measuring changes in fecal microbiota, total gas production and formation of common SCFAs. Fecal donations were collected from three healthy volunteers. Materials analyzed included: pure beta-glucan, Oatwell (commercially available oat-bran containing 22% oat β-glucan), xylooligosaccharides (XOS), WholeFiber (dried chicory root containing inulin, pectin, and hemi/celluloses), and pure inulin. Oatwell had the highest production of propionate at 12 h (4.76 μmol/mL) compared to inulin, WholeFiber and XOS samples (p<0.03). Oatwell’s effect was similar to those of the pure beta-glucan samples, both samples promoted the highest mean propionate production at 24 h. XOS resulted in a significant increase in the genus Bifidobacterium after 24 h of fermentation (0 h: 0.67 OTUs; 24 h: 5.22 OTUs; p = 0.038). Inulin and WholeFiber increased the beneficial genus Collinsella, consistent with findings in clinical studies. All analyzed compounds were fermentable and promoted the formation of beneficial SCFAs.

Beta-carotene is a fat-soluble antioxidant commonly found in foods such as fruits, vegetables, and palm oil. Despite various liquid chromatography methods are proposed to detect and measure the sera carotenoid level, a long retention time to elute this marker is needed. This study attempted to develop a rapid reverse phase method in eluding beta-carotene in human sera. The researchers managed to elute the antioxidant in 2.2 minutes by applying a combination of a C8 column, mobile phase comprising of acetonitrile mixed with methanol in 70:30 proportion, and an ultra-high performance liquid chromatography system. The outputs had a good calibration curve (R²=0.959) and low coefficient of variation (0.2%), suggesting this protocol is reliable. A column with a lower carbon chain such as C8 allows the beta-carotene molecule to flow through the column faster. Besides, selecting solvents with high elution strength coupled with an ultra-high performance liquid chromatography system which equipped with high pressure can force the beta-carotene through the column in a shorter duration compared to previous reported methods. Therefore, it is recommended to adopt this protocol in epidemiological studies where beta-carotene is screened as a dietary biomarker associated with disease of interest by using human sera in the population level.

During type 1 diabetes mellitus (T1DM) development, beta-cells undergo intense endoplasmic reticulum (ER) stress that could result in apoptosis through the failure of adaptation to the unfolded protein response (UPR). Islet transplantation is considered an attractive alternative among beta-cell replacement therapies for T1DM. To avoid the loss of beta-cells that will jeopardize the transplant´s outcome, several strategies are being studied. We have previously shown that prolactin induces protection against pro-inflammatory cytokines and redox imbalance-induced beta-cell death by increasing heat shock protein B1 (HSPB1) levels. Since the role of HSPB1 in beta cells has not been deeply studied, we investigated the mechanisms involved in unbalanced protein homeostasis caused by intense ER stress and overload of the proteasomal protein degradation pathway. We tested whether HSPB1-mediated cytoprotective effects involved UPR modulation and improvement of protein degradation via the ubiquitin-proteasome system. We demonstrated that increased levels of HSPB1: attenuated levels of pro-apoptotic proteins like CHOP and BIM, increased protein ubiquitination and the speed of proteasomal protein degradation. Our data showed that HSPB1 induced resistance to proteotoxic stress and thus enhanced cell survival via an increase in beta-cell proteolytic capacity. These results could contribute to generate strategies aiming at optimization of beta-cell replacement therapies.