In this paper, we introduced a generalized ∆-implicit locally contractive condition and give some examples to support it and to show its significance in fixed point theory. We prove that the mappings satisfying generalized ∆-implicit locally contractive condition admits a common fixed point, where, the ordered multiplicative GM−metric space is chosen as underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show existence of solutions to a system of nonlinear -Volterra type- integral equations.

Mechanical properties of cardiomyocytes from different transmural regions are heterogeneous in the left ventricular wall. The cardiomyocyte mechanical environment affects this heterogeneity because of mechano-electric feedback mechanisms. In the present study, we investigated the effects of load upon transmural differences in contraction of subendocardial (ENDO) and subepicardial (EPI) single cells isolated from the murine left ventricle. Various loads were applied to the cells using carbon fiber techniques for single myocytes. To simulate experimentally obtained results and to predict mechanisms underlying the cellular response to change in load, our mathematical models of the ENDO and EPI cells were used. Extent of the transmural gradient in the time course of contractions was independent of the loading conditions where unloaded and heavy loaded (isometric) contractions were examined, but the regional gradient of the relaxation time characteristics tended to decrease when the load decreased. Under auxotonic contractions, time to peak contraction (T_max) was significantly longer in ENDO cells than in EPI cells at low preload. An increase in preload (axial stretch) prolonged T_max in both cell types; however, the prolongation was greater in EPI cells, resulting in a decrease in transmural gradient in T_max at high preload. The [Ca²⁺]_i transient decay time constant was consistent with the greater preload dependency in T_max of EPI cells. Our modified mathematical models reproduced experimental results, suggesting that differences in cooperativity of cross bridges and calcium troponin C complex interactions between the ENDO and EPI cardiomyocytes may contribute to the different cellular responses to stretch, which may provide a decrease in transmural dispersion of cellular shortening in the intact heart.

The golden ratio, also known as Phi (ϕ ≈ 1.618034), attracted the interest of mathematicians, artists, and intellectuals for many centuries, probably from when it was discovered in human anthropometry. Even in recent times, researchers found the presence of golden ratio in Renaissance paintings and aesthetic preferences. The reasons behind the fascination with the golden ratio remain unclear, but it has been suggested that stimuli containing this proportion are often perceived as beautiful. However, evidence is conflicting, and the literature struggles to establish the existence of individual preferences for golden ratio. To gain new insights into the nature of these preferences, one hundred participants completed an implicit association task, with either golden ratio or random stimuli presented with positive or negative words. Participants initially categorized the stimuli based on their assigned categories. Then, we assessed their explicit preferences by asking to rate the stimuli in terms of pleasantness and by completing a line bisection task and the Ultimate Game. The results revealed the typical effects observed in implicit association tasks, with improved response times and accuracy when golden ratio stimuli were associated with positive word categories. In contrast, explicit ratings yielded mixed results. We discuss our findings in relation to previous studies that have explored this issue, highlighting the ongoing debate surrounding preferences for the golden ratio.

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.

On January 1, 2024, a large earthquake occurred in Japan’s Noto region. Many buildings collapsed as a result of violent shaking. Electricity and water supplies were cut off and communications were disrupted. Immediately after the earthquake, we visited Noto and conducted disaster-relief activities. This report integrates and discusses the results of the site visits, information broadcasts by public institutions, and previous research. Evacuation centers lacked water and proper sanitation, leading to health issues, including infectious diseases. Disaster Medical Assistance Teams (DMAT) were delayed in implementing infection control measures. Isolated evacuation centers faced communication and supply challenges. Infrastructure restoration, power supply, and toilet facilities at evacuation centers were delayed because of geographical challenges. There was a lack of intervention by medical professionals in evacuation centers because the DMATs were forced to invest manpower in rescue operations. It is important to have a team that can determine and carry out the necessary activities on site, even without instructions from the DMAT. It is believed to be effective to decide in advance how volunteer teams and the private sector will conduct their activities, assuming that they will be unable to contact public institutions during a disaster. In large-scale disasters, evacuees must operate evacuation centers autonomously. To achieve this, it is necessary for residents to form healthy communities regularly. A serious disaster is expected to soon occur in Japan. We hope that the experience of this disaster will be useful for preparing for future disasters.

ABSTRACT After locavore was chosen as “the best word of the year” in 2007, its popularity increased gradually. Today great number of locavores consciously prefer locally produced food for the benefit of themselves and their community. Undoubtedly this conscious movement has its consequences in marketing discipline. Accordingly, this paper is purposed to examine the how locavore perceptions affect loyalty towards retailers that sell locally produced food. In this context, a survey was applied to people residing in Istanbul and Kocaeli districts to measure the robustness of these effects. Furthermore, attitude towards locavore is used as a control variable to reveal to what extend locavorism affects these proposed connections. According to results, for participants with low attitude, Social Responsibility and Health Consciousness variables have significant effect on local retailer shopping loyalty. However, for participants with high attitude, all independent variables proved to have substantial effect on local retailer shopping loyalty. As the first empirical study in Turkey on the subject, this paper will provide important insight to academia and practicioners due to today’s ever-increasing consciousness in green marketing.

Proper calibration of eye movement signal registered by an eye tracker seems to be one of the main challenges in popularizing eye trackers as yet another user input device. Classic calibration methods taking time and imposing unnatural behavior of users have to be replaced by intelligent methods that are able to calibrate the signal without conscious cooperation with users. Such an implicit calibration requires some knowledge about the stimulus a person is looking at and takes into account this information to predict probable gaze targets. The paper describes one of the possible methods to perform implicit calibration: it starts with finding probable fixation targets (PFTs), then uses these targets to build a mapping - probable gaze path. Various possible algorithms that may be used for finding PFTs and mapping are presented in the paper and errors are calculated utilizing two datasets registered with two different types of eye trackers. The results show that although for now the implicit calibration provides results worse than the classic one, it may be comparable with it and sufficient for some applications.

PURPOSE: Breast cancer tumors frequently have intratumor heterogeneity. Tumors with high intratumor heterogeneity have caused therapeutic resistance and have human epidermal growth factor receptor 2 (HER2) heterogeneity in response to HER2-targeted therapies. This study aimed to investigate whether high HER2 heterogeneity levels were clinically related to poor prognosis for HER2-targeted adjuvant therapies resistance in primary breast cancers. METHODS: This study included patients with primary breast cancer (n = 251) treated with adjuvant HER2-targeted therapies. HER2 heterogeneity was manifested by the shape of HER2 fluorescence in situ hybridization amplification (FISH) distributed histograms with HER2 gene copy number within a tumor sample. Those heterogeneity classified each tumor into the biphasic grade graph (high heterogeneity [HH]) group and the monophasic grade graph (low heterogeneity [LH]) group. Both groups were evaluated for disease-free survival (DFS) and overall survival (OS) for a median of ten years of annual follow-up. RESULTS: Of 251 patients with HER2-positive breast cancer, 46 (18.3%) and 205 (81.7%) were classified into the HH and LH groups, respectively. The HH group had more distant metastases and a poorer prognosis than the LH group (DFS: P < 0.001 (HH:63% vs LH:91% at 10 years), and OS: P = 0.012 (HH:78% vs LH:95% at 10 years). CONCLUSION: High HER2 heterogeneity is a poor prognostic factor in patients with HER2-positive breast cancer. A novel approach of heterogeneity, which is manifested by the shape of HER2 FISH distributions, might be clinically useful in the prognosis prediction of patients after HER2 adjuvant therapy.

In this paper we focus on an implicit assumption in the BSM framework that limits the scope of market network connections to seeking gains in the currency basis, i.e., on trading strategies between the numeraire and the stock and between the numeraire and the option, separately. We relax this assumption and derive the equivalent of the standard BSM approach under a more general market network framework in order to assess its implications. In doing so, we find that it is not possible to hedge the implicit option that allows one to directly trade the option and stock. This represents a potential challenge to the BSM framework, since the missing market network connection provides a potentially useful mechanism for risk-bearing portfolio managers to alter their portfolios.

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 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.

Rectal cancer presents a significant burden globally, often requiring multimodal therapy for locally advanced cases. Long-course chemoradiotherapy (LCRT) and short-course radiotherapy (SCRT) followed by surgery have been conventional neoadjuvant approaches. Recent trials favor LCRT due to improved local control. However, tumor distant recurrence remains a concern, prompting exploration of Total Neoadjuvant Therapy (TNT) as a comprehensive treatment strat-egy. Immune checkpoint inhibitors (ICIs) show promise, particularly in mismatch repair-deficient (dMMR) or microsatellite instability-high (MSI-H) tumors, potentially revolutionizing neoadjuvant regimens. Non-operative management (NOM) represents a viable alternative post-neoadjuvant therapy for selected patients achieving clinical complete response (cCR). Additionally, monitoring minimal residual disease (MRD) using circulating tumor DNA (ctDNA) emerges as a non-invasive method for treatment response assessment. This review synthesizes current evidence on TNT, ICIs, NOM and ctDNA, elucidating their implications for rectal cancer management and highlighting avenues for future research and clinical application.

We develop the theory of Heyting locally small spaces, including Stone-like dualities such as a new version of Esakia duality and a system of concrete isomorphisms and equivalences. In such a way, we continue building tame topology, realising Grothendieck's ideas. We use up-spectral spaces and define the standard up-spectralification of a Kolmogorov locally small space. This research gives more understanding of locally definable spaces over structures with topologies.

The study assessed the trapping efficacy of locally-modified 1) Gravid Aedes Trap(GAT) lined with insecticide-treated net (ITN) as a killing agent, 2) Autocidal Gravid Ovitrap(AGO) with sticky board in the semi-field system (SFS) and field setting. Fully-balanced Latin square experiments were conducted to compare GAT lined with ITN vs AGO, both with either yeast or grass infusion. Biogents-Sentinel (BGS) with BG-Lure and no CO2 was used as standard trap for Aedes mosquitoes. In the SFS, GAT outperformed AGO in collecting both nulliparous (65% vs 49%,OR=2.22,[95%CI:1.89-2.60],p

In this paper, the concept of fuzzy locally convex spaces generated by a family of fuzzy seminorms is introduced. We prove that a Minkowski functional of zero neighborhoods generates a seminorm and finally deduce that the topology generated by the family of seminorms coincides with that of the Minkowski functional.

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.

In nonlinear self-consistent system, Lorenz system (Lorenz equations) is a classic case with chaos solutions which are sensitively dependent on the initial conditions. As it is difficult to get the analytical solution, the numerical methods and qualitative analytical methods are widely used in many studies. In these papers, Runge-Kutta method is the one most often used to solve these differential equations. However, this method is still a method based on explicit time scheme, which would be the main reason for the chaotic solutions to Lorenz system. In this work, numerical experiments based on implicit time scheme and explicit scheme are setup for comparison, the results show that: in implicit time scheme, the numerical solutions (counterexamples) are without chaos; for an original volume, the volume shrinks exponentially fast to 0 in common.

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.

In this article some important observations have been reported on recent works related to weakly tripotent rings and locally invo-regular rings. Our findings give additional results as well as correct some recent results on weakly tripotent rings and locally invo-regular rings appeared in Rendiconti Sem. Mat. Univ. Pol. Torino (2021) and Azerbaijan Journal of Mathematics (2021) respectively. In addition we exhibit that if the Jacobson radical J(A) of a ring is strongly involution t-clean then the characteristic of J(A) need not be four. This finding improves an important result appeared in Eur. J. Pure Appl. Math (2022).

The digital orthophoto is an image with geometric accuracy and no distortion. It is acquired through a top view of the scene and finds widespread applications in map creation, planning, and related fields.This paper classifies the algorithms for digital orthophoto generation into two groups: explicit methods and implicit methods. Explicit methods rely on traditional geometric methods, obtaining geometric structure presented by explicit parameters with Multi-View Stereo (MVS) theories, as seen in our proposed Top view constrained Dense Matching (TDM). Implicit methods rely on neural rendering, obtaining implicit neural representation of scenes through the training of neural networks, as exemplified by Neural Radiance Fields (NeRF). Both of them obtain digital orthophoto by rendering from a top view perspective. In addition, this paper conducts an in-depth comparative study between explicit and implicit methods. The experiments demonstrate that both algorithms meet the measurement accuracy requirements and exhibit a similar level of quality in terms of generated results. Importantly, the explicit method shows a significant advantage in terms of efficiency, with a time consumption reduction of two orders of magnitude under our latest CUDA version TDM algorithm. Although explicit and implicit methods differ significantly in their representation forms, they share commonalities in the implementation across algorithmic stages. These findings highlight the potential advantages of explicit methods in orthophoto generation, while also providing beneficial references and practical guidance for the fast digital orthophoto generation using implicit methods.

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.

This paper presents a numerical method for solving a two-dimensional subdiffusion equation with a Caputo fractional derivative. The problem considered assumes symmetry in both the equation’s solution domain and the boundary conditions, allowing for a reduction of the two-dimensional equation to a one-dimensional one. The proposed method is an extension of the fractional Crank-Nicolson method, based on the discretization of the equivalent integral-differential equation. To validate the method, the obtained results were compared with a solution obtained through Laplace transform. The analytical solution in the image of the Laplace transform was inverted using the Gaver-Wynn-Rho algorithm implemented in the specialized mathematical computing environment, Wolfram Mathematica. The results clearly show the mutual convergence of the solutions obtained by the two methods.

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.

A new coordinate system based on the proper times of rest frames in the Schwarzschild metric is developed to show that a radially falling worldline becomes light-like at the event horizon in the Schwarzschild metric. This system has no coordinate singularity at the event horizon and light travels on 45 degree lines everywhere in the space. The light-like nature of the worldline is confirmed by analyzing it in Kruskal-Szekeres (KS) coordinates. It is shown that the worldline in KS coordinates has an undefined derivative at the horizon at any point other than the origin of the KS coordinates. It is then demonstrated that the origin of the KS coordinate system can be reached in the falling frame by exploiting the time symmetry of the manifold and that the falling worldline is indeed light-like there. The light-like nature of the worldline means that the horizon is length contracted to a point in the falling frame, such that the event horizon is proven to be the source of the Schwarzschild metric and the end point of gravitational collapse.

Incremental stability analysis for time-delay systems has attracted more and more attentions for its contemporary applications in transportation processes, population dynamics, economics, satellite positions, etc. This paper researches criteria on v(t)-incremental stability, which is defined to demonstrate the convergence rate for incremental stability, for time-delay systems. Firstly, the sufficient conditions for v(t)-incremental stability for time-delay systems with continuous right-hands are studied, and several corollaries for specific cases are provided. As for time-delay systems with discontinuous right-hands, after expounding the relevant conditions for the existence and uniqueness of the Filippov solution, by using approximation methods, sufficient conditions for v(t)-incremental stability are obtained. The conclusions are applied to linear switched time-delay systems and Hopfield neural network system with composite right-hand afterwards.

Myoelectric control is the cornerstone of many assistive technologies used in clinical practice, such as prosthetics and orthoses, and human-computer interaction, such as virtual reality control. Although the performance of such devices exceeds 90\% in controlled environments, myoelectric devices still face challenges in robustness to variability of daily living conditions. Within this survey, the intrisic physiological mechanisms limiting practical implementations of myoelectric devices were explored: the limb position effect and the contraction intensity effect. The degradation of electromyography (EMG) pattern recognition in the presence of these factors was demonstrated on six datasets, where performance was 13% and 20% lower in realistic environments compared to controlled environments for the limb position and contraction intensity effect, respectively. The experimental designs of limb position and contraction intensity literature were surveyed. Current state-of-the-art training strategies and robust algorithms for both effects were compiled and presented. Recommendations for future limb position effect studies include: the collection protocol providing exemplars of 6 positions (four limb positions and three forearm orientations), three-dimensional space experimental designs, transfer learning approaches, and multi-modal sensor configurations. Recommendations for future contraction intensity effect studies include: the collection of dynamic contractions, nonlinear complexity features, and proportional control.

The article is devoted to infinitesimal transformations. We have obtained that LCK-manifolds do not admit nontrivial infinitesimal projective transformations. Then we study infinitesimal conformal transformations of LCK-manifolds. We have found the expression for the Lie derivative of a Lee form. Also we have obtained the system of partial differential equations for the transformations, and explored its integrability conditions. Hence we have got the necessary and sufficient conditions in order that the an LCK-manifold admits a group of conformal motions. Also we have calculated the number of parameters which the group depends on. We have proved that a group of conformal motions admitted by an LCK-manifold is isomorphic to a homothetic group admitted by corresponding K\"{a}hlerian metric. We also established that an isometric group of an LCK-manifold is isomorphic to a some subgroup of homothetic group of the coresponding local K\"{a}hlerian metric.

In this work, we introduce a new concepts for $\alpha$-type $F$-Suzuki contraction and $\alpha$-type $F$-weak-Suzuki contraction in the context of $b$-metric spaces. Compared to the $\alpha$-type $F$-contraction and $F$-Suzuki contraction mappings, these contractions are essentially weaker. For these type of contraction mappings, sufficient conditions are established for the fixed point's existence and uniqueness in $b$-metric spaces. As a result, the findings encompass several generalizations. To show the usability of our obtained results, we provide a supportive example and an application to a non-linear differential equation with fractional order.

The protection of electronics against environmental influences and mechanical loads is important for integration of conventional electronics in textile conductive tapes. For this purpose, the sensors on the tapes are molded with plastic locally. This process step is recognized in the injection molding process. The molding compound is then later selected depending on: The field of application, the parameters of the manufacturing process and the textile tape properties. We have designed a mould for liquid silicone (LSR) as well as for the textile and electronic insertions. The cavities are sealed by a local compression of the textile and the two inserts are positioned with position pins representing the main aspect of the mould design. The sampling tool and the process parameter optimization are mainly based on the material properties of the silicone and the mechanical sensitivity of the inserts. To reduce the deformation of the circuit boards by the melt front and ensuring the functionality of the electronics a low-pressure process is used.

In this paper, some characterizations of fuzzifying strong compactness are given, including characterizations in terms of nets and pre -subbases. Several characterizations of locally strong compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

In this work, we incorporate a thixotropic-viscoelastic model into the widely used Computational Fluid Dynamics (CFD) software OpenFOAM, along with the rheoTool library. The model we implement is known as the Modified-Bautista-Manero (MBM), and effectively describes the rheological behavior of worm-like micellar solutions in extensional flows. We provide a detailed explanation of the numerical implementation of the model, specifically using the log-conformation tensor approach. Unlike previous works focused on this kind of fluids, we simulate inertial flows while considering convective terms in the governing equations, thus obtaining a more realistic behavior on the calculated results. The MBM model implementation is validated through numerical simulations on two different industrial-relevant geometries: the planar 4:1 contraction and the 4:1:4 contraction-expansion configurations. Furthermore, we investigate the influence of inertial, viscoelastic, and thixotropic effects on various flow field variables. These variables include velocity, viscosity, normal stresses, and corner vortex size. Our analysis encompasses both transient and steady solutions of corner vortexes across a range of Deborah and Reynolds numbers. Our results are also directly compared with simulations obtained using the non-thixotropic rubber network-based exponential Phan-Thien-Tanner (EPTT) model. From our planar 4:1 contraction results, we found that vortex-enhancement is seen when high elasticity is coupled with quick structural reformation and very low inertial effects. From our planar 4:1:4 contraction-expansion simulations, we show that an increase in inertia leads both to vortex-inhibition in the upstream channel and slight vortex-enhancement in the downstream channel. Lastly, we show the strong effect of the convection of fluidity into the fluidity profiles and into the upstream/downstream corner vortex sizes.

Reliable and robust control of power converters is a key issue in the performance of numerous technological devices. In this paper we show a design technique for the control of a DC-DC buck converter with a switching technique that guarantees not only good performance but also global stability. We show that making use of the contraction theorem in the Jordan canonical form of the buck converter, it is possible to find a switching surface that guarantees stability but it is incapable of rejecting load perturbations. To overcome this, we expand the system to include the dynamics of the voltage error and we demonstrate that the same design procedure is not only able to stabilize the system to the desired operation point but also to reject load, input voltage and reference voltage perturbations.

Continuum robots play the role of end-effector in various surgical robots and endoscopic devices. The robots may be categorized as rigid or soft continuum robots (SCRs). While the SCRs have proven advantages such as safety and compliance, more research and development are required to enhance their capability for specific medical scenarios. This research aims at designing a soft robot considering concepts of geometric and kinematic similarities. The chosen application is a semi-invasive medical application known as Transesophageal Echocardiography (TEE), but the methodology can be implemented in other similar applications. Since established rigid carrier construction make use of principles we find as well embodied in vertebral spines, the paragon for soft robot solution can be the phylogenetic precursor of the spine, the Chorda dorsalis. The feasibility of fabrication of a soft endoscopic device derived from that paragon within a robotics laboratory was shown empirically by producing a three-segment pneumatic SCR. The kinematic model was proposed based on the method of transformation matrices, and an algorithm based on a self-organizing map (SOM) was proposed and applied to realize kinematic similarity. The simulation results indicate that the algorithm acting as an open-loop controller forces the soft robot tip to follow the desired path which in this case is the path of the rigid probe. It is concluded that the solution provides a soft robot that can surrogate and succeed the traditional rigid counterpart owing to size, workspace, and kinematics.

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.

Pairs of potential and flow variables have long been established for interfacing object-oriented component models of physical systems. Recently, however, the use of triplets has been discovered for the purpose of robust modeling. New and powerful Modelica libraries have been developed such as the DLR ThermoFluid Stream library or the introduction of the Dialectic Mechanics library. Their use of triplets is entangled with a special modeling approach that uses Linear Implicit Equilibrium Dynamics. In this paper, we study the basic motivation of this approach, its benefits and drawbacks before we finally demonstrate how it beneficially impacts the generation of corresponding simulation code.

If "quantization is an art" then it can be greatly rened by adopting cyclic time formalism. In past papers we have proven the effectiveness of a formulation of physics based on cyclic relativistic time. Now we can demonstrate in a general way, by using theorems of Geometric Quantization, that the Poisson brackets of intrinsically cyclic time dynamics directly imply the ordinary canonical commutation relations and the other Dirac's rules of canonical Quantum Mechanics. In other words, according to our result, canonical quantization is an implicit way of imposing intrinsically cyclic time dynamics without explicitly saying that time is a cyclic dimension.

Accurate climate data at fine spatial resolution are essential for scientific research and the development and planning of crucial social systems, such as energy and agriculture. Among them, sea surface temperature plays a critical role as the associated El Niño-Southern Oscillation (ENSO) is considered a significant signal of global interannual climate system. In this paper, we propose an implicit neural representation-based interpolation method with temporal information (T_INRI) to reconstruct climate data of high spatial resolution, with sea surface temperature as the research object. Traditional deep learning models for generating high-resolution climate data are only applicable to fixed resolution enhancement scales. In contrast, the proposed T_INRI method is not limited to the enhancement scale provided during the training process and its results indicate that it can enhance low-resolution input by arbitrary scale. Additionally, we discuss the impact of temporal information on the generation of high-resolution climate data, specifically, which month the low-resolution sea surface temperature data is from. Our experimental results indicate that T_INRI is advantageous over traditional interpolation methods under different enhancement scales, and the temporal information can improve T_INRI performance for a different calendar month. We also examined the potential capability of T_INRI in recovering missing grid value. These results demonstrate that the proposed T_INRI is a promising method for generating high-resolution climate data and has significant implications for climate research and related applications.

The computing power of smartphones has not received considerable attention in the mainstream education system. Most of the education-oriented smartphone applications (apps) are limited to general purpose services like Massive Open Online Courses (MOOCs), language learning, and calculators (performing basic mathematical calculations). Greater potential of smartphones lies in educators and researchers developing their customized apps for learners in highly specific domains. In line with this, we present Fluid Dynamics, a highly accurate Android application for measuring flow properties in compressible flows. This app can determine properties across the stationary normal and oblique shock, moving normal shock and across Prandtl $-$ Meyer expansion fan. This app can also measure isentropic flows, Fanno flows, and Rayleigh flows. The functionality of this app is also extended to calculate properties in the atmosphere by assuming the International Standard Atmosphere (ISA) relations and also flows across the Pitot tube. Such measurements are complicated and time-consuming since the relations are implicit and hence require the use of numerical methods, which give rise to repetitive calculations. The app is an efficient semi-implicit solver for gas dynamics formulations and uses underlying numerical methods for the computations in a graphical user interface (GUI), thereby easing and quickening the learning of concerned users. The app is designed for the Android operating system, the most ubiquitous and capable surveillance platform, and its calculations are based on JAVA based code methodology. In order to check its accuracy, the app's results are validated against the existing data given in the literature.

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.

In Holter monitoring, the precise detection of standard heartbeats and Ventricular Premature Contractions (PVCs) is paramount for accurate cardiac rhythm assessment. This study introduces a novel application of the 1D U-Net neural network architecture aimed at enhancing PVC detection in Holter recordings. Training data comprised the Icentia11k, INCART DB, and our custom dataset. The model’s efficacy was subsequently validated against traditional Holter analysis methodologies across multiple databases, including AHA DB, MIT 11 DB, NST, and another custom dataset encompassing challenging real-world examples. The results underscored the 1D U-Net model’s prowess in QRS complex detection, achieving near-perfect balanced accuracy scores across all databases. PVC detection exhibited variability, with balanced accuracy scores ranging from 0.909 to 0.986. Despite some databases, like the AHA DB, showcasing lower sensitivity metrics, their robust balanced accuracy accentuates the model’s equitable performance in discerning both false positives and negatives. In conclusion, while the 1D U-Net architecture is a formidable tool for QRS detection, there’s a clear avenue for further refinement in its PVC detection capability, given the inherent complexities and noise challenges in real-world PVC occurrences.

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.

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.

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.

Empirical Colebrook equation from 1939 is still accepted as an informal standard to calculate friction factor during the turbulent flow (4000 < Re < 10⁸) through pipes from smooth with almost negligible relative roughness (ε/D→0) to the very rough (up to ε/D = 0.05) inner surface. The Colebrook equation contains flow friction factor λ in implicit logarithmic form where it is, aside of itself; λ, a function of the Reynolds number Re and the relative roughness of inner pipe surface ε/D; λ = f (λ, Re, ε/D). To evaluate the error introduced by many available explicit approximations to the Colebrook equation, λ ≈ f(Re, ε/D), it is necessary to determinate value of the friction factor λ from the Colebrook equation as accurate as possible. The most accurate way to achieve that is using some kind of iterative methods. Usually classical approach also known as simple fixed point method requires up to 8 iterations to achieve the high level of accuracy, but does not require derivatives of the Colebrook function as here presented accelerated Householder’s approach (3^rd order, 2^nd order: Halley’s and Schröder’s method and 1^st order: Newton-Raphson) which needs only 3 to 7 iteration and three-point iterative methods which needs only 1 to 4 iteration to achieve the same high level of accuracy. Strategies how to find derivatives of the Colebrook function in symbolic form, how to avoid use of the derivatives (Secant method) and how to choose optimal starting point for the iterative procedure are shown. Householder’s approach to the Colebrook’s equations expressed through the Lambert W-function is also analyzed. One approximation to the Colebrook equation based on the analysis from the paper with the error of no more than 0.0617% is shown.

Traditional Corporate Social Responsibility (CSR)-programs rarely include participatory components that connect CSR-activities of private companies with their local communities. However, there is an increasing demand to include citizens as well as the resources and expertise of the private sector in the design and implementation of local community planning processes. To assess the potential, opportunities, and challenges of including private companies into participatory community planning at a local level, we analyzed the experiences that we collected during the piloting phase and the commercial roll-out of the ‘Bürgercockpit’-application for citizen participation, as well as the results of a digital CSR-questionnaire that we shared with different companies in Austria. Our research indicates that most of the participating companies are interested in including local communities into their CSR-projects using a digital tool, if this tool is easy-to-use, easy-to-access, and provides a flexible structure to address specific project requirements as well as properly designed features for stakeholder communication and user feedback. The findings of both, the ‘Bürgercockpit’-pilot study and the CSR-questionnaire provided us valuable input for designing a prototype solution of a digital CSR-tool for participatory community planning at a local level as well as recommendations for future research in this topic of growing interest.

The vagina is an essential component of the female reproductive system and is responsible for providing female sexual satisfaction. Vaginal smooth muscle contraction plays a crucial role in various physiological processes, including sexual arousal, childbirth, and urinary continence. In pathophysiological conditions such as pelvic floor disorders, aberrations in vaginal smooth muscle function can lead to urinary incontinence and pelvic organ prolapse. A set of cellular and sub-cellular physiological mechanisms regulates the contractile properties of the vaginal smooth muscle cells. Calcium influx is a crucial determinant of smooth muscle contraction, facilitated through voltage-dependent calcium channels and calcium release from intracellular stores. Comprehensive reviews on smooth muscle biophysics are relatively scarce within the scientific literature, likely due to the complexity and specialized nature of the topic. The objective of this review is to provide a comprehensive description of alterations in the cellular physiology of vaginal smooth muscle contraction. The benefit associated with this particular approach is that conducting a comprehensive examination of the cellular mechanisms underlying contractile activation will enable the creation of more targeted therapeutic agents to control vaginal contraction disorders.

The transport and entanglement of photons is becoming prominent in optics applied to information and quantum computing, where the angular momentum of light stands out in the exchange and inversion of quantized states, with prospects for several technological applications, such as the transport and storage of quantum information. In order to contribute to the understanding of quantized states in photon-matter interaction, we describe a quantized state equation in multidimensional Hilbert space for the diagnosis of OAM states, where probabilities arise in a relativistic setting. It was found that the classical-relativistic variability of the probabilities constitutes a resultant capable of describing the quantized states of light, where the state variable is the variation of the angular momentum of the photon, capable of estimating the orbital angular momentum inversion points at angular incidence. It was found that the chances of finding the quantized states of light at angular incidence can be treated by purely relativistic probabilities, explaining that when both states have equal chances of being found and the angular momentum variation is zero, the source-observer synchronizations occur at the step of increasing relativistic regime of the photon dynamics. We found that the relativistic effect from the perspective of the source referential is able to alter the chances of an event occurring, dilating and contracting the probabilities of finding a quantized state of light at angular incidence.

The editors of several major journals have recently asserted the importance of combating racism and sexism in science. This is especially relevant now, as the COVID-19 pandemic may have led to a widening of the gender and racial/ethnicity gaps. Implicit bias is a crucial component in this fight. Negative stereotypes that are socially constructed in a given culture are frequently associated with implicit bias (which is unconscious or not perceived). In the present article, we point to scientific evidence that shows the presence of implicit bias in the academic community, which contributes to strongly damaging unconscious evaluations and judgments of individuals or groups. Additionally, we suggest several actions aimed at (1) editors and reviewers of scientific journals, (2) people in positions of power within funding agencies and research institutions and (3) members of selection committees to mitigate this effect. These recommendations are based on the experience of a group of Latin American scientists comprising Black and Latin women, teachers and undergraduate students who participate in a women in science working group at universities in the state of Rio de Janeiro, Brazil. With this article, we hope to contribute to reflections, actions and the development of institutional policies that enable and consolidate diversity in science and reduce disparities based on gender and race/ethnicity.

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.

Pito is a traditionally brewed alcoholic beverage in some African countries. It is gaining much prominence and the patronage among the youth. Therefore, samples of the drink were collected every week for six weeks from three different popular brewing sites at Lower Prampram in the Ningo-Prampram District of Accra, Ghana. The samples were processed and examined for bacteria and fungi using the Standard Plate Count (SPC) technique. A total of six different bacteria and a fungus were isolated. The bacteria were Escherichia coli, Klesiella pneumoniae, Shigella spp, Enterobacter aerogenes, Staphylococcus aureus and Pseudomonas aeroginosa, whiles the fungus was Saccharomyces cerevisiae. Total viable counts as well as individual isolates counts in all the pito samples were found to be less than 104 cfu/ml. It is noteworthy that, Saccharomyces cerevisiae, the only fungus isolated is known to be associated with fermentation and the microbes isolated from the pito samples were found to be within the permissible limits. However, these potentially pathogenic microbes, if found in unacceptable limits, from the fermenting samples could merit public health attention. Therefore, periodic screening of pito and their brewers, coupled with education on the maintenance of recommended guidelines concerning food and drink production is encouraged.

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.

Purpose: While resultant maximal voluntary contraction (MVC) is commonly used to assess muscular performance, the simultaneous activation of antagonist muscles could dramatically underestimate the strength of the agonist muscles. While quantification of antagonist torque has been performed in plantar- (PF) and dorsi-flexion (DF) joint in isometric conditions, it has yet to be determined in anisometric (concentric and eccentric) conditions. Methods: The experiment was performed in 9 participants through 2 sessions (reliability). The MVCs in DF and PF were measured in isometric, concentric and eccentric conditions (10°.s^-1). Electromyographic (EMG) activities from the soleus, gastrocnemius medialis and lateralis, and tibialis anterior muscles were simultaneously recorded. The EMG biofeedback method was used to quantify antagonist torque, where participants were asked to maintain a level of EMG activity, corresponding to antagonist EMG activity and related to the muscle contraction type, according to a visual EMG bio-feedback displayed on a screen. Results: Resultant torque significantly underestimated agonist torque in DF MVC (30-65%) and to a lesser extent in PF MVC (3%). Triceps surae antagonist torque was significantly modified with muscle contraction type, showing higher antagonist torque in isometric (29 Nm) than eccentric (23 Nm, p < 0.001) and concentric (14 Nm, p < 0.001) conditions and resulting in modification of the DF MVC torque-velocity shape. The difference between DF eccentric and concentric MVC was attenuated when considered agonist torque (12%) rather than resultant torque (45%). Conclusion: Estimation of the antagonist torque in isometric or anisometric condition brings new insights to assessment of muscular performance and could result in costly misinterpretation in strength training and/or rehabilitation programs.

Assuming a geometrically closed universe, we predict a value for the cosmic curvature, , a value within current observational bounds. We also propose a thermodynamic heat engine model for the universe, which bypasses the need for an inflaton field. Our model is based on a Carnot Cycle where we have isothermal expansion, followed by adiabatic expansion, followed by isothermal contraction, followed by adiabatic contraction, bringing us back to our original starting point. For the working substance, we focus specifically on the CMB radiation filling the collective voids in the universe. Using this construct, we identify cosmic inflation as the isothermal expansion phase, which lasts just under, . The collective CMB volume we see today only increases by a factor of 5.65 times during this process, and homogeneity and perturbations in the CMB are explained. The singularity problem is avoided and we have a clear mechanism for the work done by the cosmos in causing expansion, and later contraction. For scaling laws with respect to the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, , the smeared cosmic susceptibility, decreases with increasing cosmic scale parameter, . Within this framework, we can predict a maximum Hubble volume with minimum CMB temperature for the voids before contraction begins, as well as a minimum volume with maximum CMB temperature when expansion starts. The thermodynamic heat cycle deviates from efficiency in converting heat energy into mechanical energy (expansion) by a minuscule amount, namely, . The significance of this number is not known.

How language mediates emotional perception and experience is poorly understood. The present event-related potential (ERP) study examined the explicit and implicit processing of emotional speech to differentiate the relative influences of communication channel, emotion category and task type in the prosodic salience effect. Thirty participants (15 women) were presented with spoken words denoting happiness, sadness and neutrality in either the prosodic or semantic channel. They were asked to judge the emotional content (explicit task) and speakers’ gender (implicit task) of the stimuli. Results indicated that emotional prosody (relative to semantics) triggered larger N100 and P200 amplitudes with greater delta, theta and alpha inter-trial phase coherence (ITPC) values in the corresponding early time windows, and continued to produce larger LPC amplitudes and faster responses during late stages of higher-order cognitive processing. The relative salience of prosodic and semantics was modulated by emotion and task, though such modulatory effects varied across different processing stages. The prosodic salience effect was reduced for sadness processing and in the implicit task during early auditory processing and decision-making but reduced for happiness processing in the explicit task during conscious emotion processing. Additionally, across-trial synchronization of delta, theta and alpha bands predicted the ERP components with higher ITPC values significantly associated with stronger N100, P200 and LPC enhancement. These findings reveal the neurocognitive dynamics of emotional speech processing with prosodic salience tied to stage-dependent emotion- and task-specific effects, which can reveal insights to research reconciling language and emotion processing from cross-linguistic/cultural and clinical perspectives.

To solve the problem of low efficiency of source seeking in implicit information field, this paper presents an autonomous souring method based on balanced searching strategy is enlighten by biological homing behaviors. At the beginning of the research, the source seeking task come down to a multi-objective convergence issue. By taking the feasibility search behaviors as the individual sample of the evolutionary population drawing on the thought of evolutionary algorithms, then combine motion searching with population evolution, so the carrier can be guide to complete source seeking task by solving the multi-objective problem. Furthermore, the distribution entropy is also considerated d to measure the searching bias in the process of source seeking. Combined with the demand of the source seeking process, a new source seeking method of balanced searching strategy is designed. Ultimately, through theoretical analysis and simulation verification confirm the effectiveness and rationality of the proposed method.

Recent studies have shown that the mechanical properties of bioinspired periodic composite materials can be strongly influenced by finite deformation effects, leading to highly nonlinear static and dynamic behaviors at multiple length scales. For instance, in porous periodic nacre-like microstructures, microscopic and macroscopic instabilities may occur for a given uniaxial loading process and, as a consequence, wave attenuation properties may evolve as a function of the microstructural evolution, giving it the designation of metamaterials. The numerical outcomes provide new opportunities to design bioinspired soft composite metamaterials characterized by high deformability and enhanced elastic wave attenuation capabilities given by the insertion of voids and lead cores.

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.

Background: Locally advanced rectal cancers (10-20%) can present with infiltration into adjacent viscera. R0 resections remain the key factor for better survival. Traditionally these cases have been managed with open surgery. There are some limitations of laparoscopic surgery in these case, which can potentially be overcome by robotic surgery. Objectives: To determine the feasibility and outcome results of robotic multi-visceral resection of stage T4 rectal carcinoma. Methods: Consecutive patients having locally advanced carcinoma of rectum, who undergone robotic multi-visceral resection as the primary treatment between 2015 -2018 were included, through our database which was maintained prospectively. All perioperative and intraoperative parameters were analyzed. Patient demographics, co-morbidities, preoperative imaging, endoscopic findings, operative data, histopathology results, postoperative hospital course and procedure related postoperative adverse events were noted and analyzed. Results: Twenty-one patients with the diagnosis of nonmetastatic locally advanced rectal cancers were operated with Robotic Si/X platform. The median body mass index was 28.5 kg/m2 (range 21-42). The mean blood loss during operation was 20 ml (range 5-200), and the mean duration of surgery was 280 min (range 240-430). The median hospital stay after operation was 6 days (range 4-25 days). On postoperative histopathology, R0 resection rate was 90.5% (19/21). Conclusions: The robotic multi-visceral en-bloc resection of stage T4 rectal carcinoma is technically feasible and oncologically safe. Advanced technical skills, accurate radiological staging and careful patient selection can allow the extension of minimal access surgery to this challenging group of patients.

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.

The cyclic universe theory is a model of cosmic evolution according to which the universe undergoes endless cycles of expansion and cooling, each beginning with a big bang and ending in a big crunch. In this paper, the researcher finds a unique property of Space-time, this particular and marvelous nature of space shows us that space can shrink, expand, and stretch. This property of space is caused the size of the Universe changing over time: growing or shrinking. The observed accelerated expansion, which relates the stretching of Shrunk space for the new theory, is derived. This model is based on three underlying notions: First, the Big Bang was not the beginning of Space-time, but rather at the very beginning fraction of a second there was an infinite force of infinite Shrunk space in the cosmic singularity, that force gave rise to the big bang and caused the rapidly growing of space-time, and all other forms of energy are transformed into matter and radiation and a new period of expansion and cooling begins. Second, there was a previous phase leading up to it, with multiple cycles of contraction and expansion that repeat indefinitely. Third, the two principal long-range forces are the gravitational force and the repulsive force generated by shrunk space. They are the two most fundamental quantities in the universe that govern cosmic evolution. They may provide the clockwork mechanism that operates our eternal cyclic universe. The space will not continue to expand forever, no need however, for dark energy and dark matter. This model of Space-time and its unique properties enables us to describe a sequence of events from the Big Bang to the Big Crunch.

In recent years, the treatment of locally-advanced rectal cancer (LARC) has been spotlighted in a number of landmark, practice-changing trials, heralding in the age of so-termed “total neoadjuvant therapy” (TNT). However, the lack of a common control arm, standard inclusion criteria, or, indeed, definition of TNT necessitates further study in this field, particularly using real-world data. We conducted a retrospective analysis of all patients treated for LARC at a single Canadian academic cancer centre between July 1st 2019 and July 14th 2022. This includes the June 2020 incorporation of TNT. 290 patients were included in the final analysis, and 124 variables were collected on each patient, including demographics, treatment type, adverse events, response to treatment, surgery versus watchful waiting and survival. Our findings demonstrate that both TNT and non-TNT regimens are highly toxic, with regards to both overall toxicity and grade 2+ adverse effects. 62 (96.9%) of patients on TNT experienced toxicities, compared to 186 (82.3%) of the non-TNT patients. Grade 2+ toxicities were 46 (71.9%) and 143 (63.3%), respectively. TNT, however, was associated with improved rates of complete response, compared to non-TNT treatment regimens (44% vs 24%). These findings suggest that TNT harbours both benefit and risk in a real-world population, and both of these aspects should be considered when deciding on a treatment approach for an individual patient. More work in the area is needed to determine longer term survival, as well as impact of surgery versus organ preservation approach on patient outcomes.

Background: The present study was carried out to evaluate the roles of proliferation and angiogenesis in locally aggressive biologic behavior of ameloblastoma versus ameloblastic fibroma; Methods: 30 formalin-fixed paraffin embedded blocks (15 cases of ameloblastoma & 15 cases of ameloblastic fibroma) were used. To evaluate the proliferation, the tissue sections were stained with AgNORs stain. CD105 was used as immunohistochemical marker of angiogenesis. Quantitative evaluations of AgNORs were performed. The mean vascular density was evaluated as a measure for CD105 protein expression by using image analyzer computer system; Results: The mean number of AgNORs dots per nucleus was significantly higher in ameloblastoma as compared to ameloblastic fibroma. Also, the protein level of CD105 showed positive expression and wide distribution that the mean vascular density was significantly higher in ameloblastoma as compared to ameloblastic fibroma; Conclusion: Quantitative evaluation of AgNORs stain & the mean vascular density utilizing CD105 protein expression may reflect a higher proliferative activity and a more locally aggressive biologic behavior of ameloblastoma when compared to ameloblastic fibroma, that other factors may be involved in biologic behavior of ameloblastic fibroma.

In this paper, we introduced many new notions and new contraction named as S-weakly contraction after that we obtained the p-common best proximity point theorems for different types of contractions in the setting of complete metric spaces by using weak P_p-property and proved the uniqueness of these points. Also we presented some examples to prove the validity of our results.

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.

A closed chain of oscillators can be considered as a model of ring-shaped ecosystems, such as atolls or coastal zones of inland reservoirs. As an oscillator model, we use the logistic map that often referred to as an archetypical example of how complex dynamics can arise from very simple nonlinear equations. We investigate the influence of the model parameters both on the nature of oscillations in the oscillator ring and on the spatial structures that arise in this case. Namely, we demonstrate a variety of emerging spatial structures depending on the initial conditions.

This paper is another applied article based on the author's "Unified Theory of Force". The main work of this paper is as follows: (1) Reinterpretation of the Lorentz contraction effect and rigorous proof that the Lorentz contraction is a physical phenomenon based on the conservation of energy and momentum under non-completely symmetrical relative motion effects. This paper proves that the Lorentz contraction effect not only occurs in the direction of motion but also simultaneously in any direction. (2) For the first time, we attempted to explain the physical meaning of the Planck energy formula in theory and associate the Planck energy formula with the Lorentz contraction effect, which can help us to have a deeper understanding of the true physical meaning behind the Planck energy formula. At the same time, we also made reasonable theoretical predictions about the basic structure of photons.

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.

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.

Radar transmit signal design is a critical factor for the radar performance. In this paper, we investigate the problem of radar signal waveform design under the small signal power conditions for detecting a doubly spread target, whose impulse response can be modeled as a random process, in a colored noise environment. The doubly spread target spans multiple range bins (range-spread) and its impulse response is time-varying due to fluctuation (hence also Doppler-spread), such that the target impulse response is both time-selective and frequency-selective. Instead of adopting the conventional assumption that the target is wide-sense stationary uncorrelated scattering,we assume that the target impulse response is both wide-sense stationary in range and in time to account for the possible correlation between the impulse responses corresponding to close range intervals. The locally most powerful detector, which is asymptotically optimal for small signal cases, is then derived for detecting such targets. The signal waveform is optimized to maximizing the detection performance of the detector or equivalently maximizing the Kullback-Leibler divergence. Numerical simulations validate the effectiveness of the proposed waveform design for the small signal power conditions and performance of optimum waveform design are shown in comparison to the frequency modulated waveform.

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.

Electrochemotherapy (ECT) is one of the newest therapeutic strategies employed as medical procedure for skin neoplasms’ treatment, especially for Classic Kaposi’s Sarcoma (CKS). The aim of this study was to demonstrate ECT clinical response and local control of CKS disease. Primary endpoint was to value the worth and efficacy of this local therapy in CKS skin lesions’ treatment. Nineteen CKS patients were enrolled, 14 males and 5 females with median age at diagnosis of 72. Complete response (CR) has been gained in 12 patients after first ECT attempt, meanwhile 3 and 4 out of 19 patients obtained a Partial response (PR), so that they underwent to a second and a third ECT treatment, each other. Clinical response was evaluated during all the time of the follow-up, which ranged between 3 months and 4 years with a median of 18 months. CKS skin lesions control still represents a challenge for surgeons and oncologists. Nevertheless, according to this and other authors’ recent experiences, ECT could be considered the gold standard strategy for early-stage patients, but at the same time it could be considered as a valid option in controlling Kaposi’s Sarcoma locally advanced lesions.

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.

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.

Gastric mixing relies both on enzymatic reactions and mechanical solicitations through antral contraction waves (ACWs). This work aims at discussing the influence of ACWs frequency and digesta viscosity on human gastric mixing efficiency by comparison with that of a soft elastic reactor (SER), that induces mixing by vibration of its wall in a similar way as ACWs promote stomach motility. The SER mixing curve was considered in order to determine the flow regime reached during gastric mixing. The number of contractions required to achieve homogenization was found to depend on the viscosity of the stomach content and the ACWs amplitude. Moreover, it was deduced from the same range of SER and ACWs operating points that the mechanical solicitation provided by human peristalsis was low and that gastric mixing was confined in laminar regime. Further efforts are needed to investigate the role of other physiological processes such as gastric secretions and emptying in overall gastric mixing performance.

A warning sign for impending cardio-vascular events is not fully established. In the process to plaque rupture, formation of vulnerable plaque is important, and oxidized cholesterols play important role in its progression. Furthermore, the significance of vasa vasorum penetrating medial smooth muscle layer and rich in atheromatous lesion should be paid attention. Cardio-ankle vascular index (CAVI) is new arterial stiffness index of the arterial tree from the origin of the aorta to the ankle. CAVI reflects functional stiffness in addition to structural stiffness. Rapid rise of CAVI means medial smooth muscle cell contraction, and strangling vasa vasorum. We reported rapid rise of CAVI in peoples after big earthquake, following high frequency of cardiovascular events. And we met several cases who showed rapid rise of CAVI a few weeks or months before suffering cardiovascular events. To explain these sequences of events, we proposed a hypothesis; A rapid rise of CAVI means medial smooth muscle contraction, strangling vasa vasorum, leading ischemia, necrosis of vulnerable plaque, then, the plaque ruptures. In individuals having high CAVI, further rapid rise of CAVI might be a warning sign for impending cardiovascular events. In such case, treatments to decrease CAVI had better to be taken soon.

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.

This study evaluated the impact of didactic videos and service user testimonial videos on mental illness stigma among medical students. Two randomized controlled trials were conducted in Nepal. Study 1 examined stigma reduction for depression. Study 2 examined depression and psychosis. Participants were Nepali medical students (Study 1:n=94, Study 2:¬n=213) randomized to three conditions: a didactic video based on the mental health Gap Action Programme (mhGAP), a service user video about living with mental illness, or a control condition with no videos. In Study 1, videos only addressed depression. In Study 2, videos addressed depression and psychosis. In Study 1, both didactic and service user videos reduced stigma compared to the control (F2,91=6.37, p=0.003). In Study 2 (depression and psychosis), there were no differences among the three arms (F2,210=2.07, p=0.13). When comparing Study 1 and 2, there was greater stigma reduction in the service user video arm with only depression versus service user videos with depression and psychosis (t(31)=-3.04, p=0.005). In summary, didactic and service user videos were associated with decreased stigma when content addressed only depression. However, no stigma reduction was seen when including depression and psychosis. This calls for different strategies based on types of mental illnesses. ClinicalTrials.gov identifier: NCT03231761

Globally, gastric cancer is a major cause of cancer mortality, with a 5-year survival rate of 32% for locally advanced and metastatic gastric cancer. This systematic literature review summarized the clinical, safety, and humanistic outcomes associated with systemic regimens given as first line therapy for locally advanced and metastatic gastric cancer. The search included articles published in English in PubMed, Embase, Web of Science, Cochrane Central Register of Controlled Trials, and the American Society of Clinical Oncology meeting library, from inception to April 2022. Phase II and III randomized controlled trials conducted among western populations diagnosed with stage III and IV locally advanced and metastatic gastric cancer were included. Two investigators independently reviewed the studies, conducted data extraction, and assessed risk of bias in accordance with PRISMA guidelines. Twenty-four randomized controlled trials totaling 8,705 patients were included. Median overall survival ranged from 5.0-13.1 months, median progression-free survival ranged from 2.0-7.7 months, and objective response ranged from 13.0-64.1%. Two studies reported higher quality of life outcomes. Grade 3 and 4 adverse events were reported in most studies. Improvement in clinical outcomes can be seen in recently published randomized controlled trials for locally advanced and metastatic gastric cancer.

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.

Inspired by the work of S. D. Odintsov and V. K. Oikonomou, Phys. Rev. D 92, 024016 (2015) [1], the present study reports a reconstruction scheme for f (R) gravity with the scale factor a(t) µ (t _* - t) _c²²describing the pre-bounce ekpyrotic contraction, where t is the big crunch time. The reconstructed f (R) is used to derive expressions for density and pressure contributions and the equation of state parameter resulting from this reconstruction is found to behave like "quintom". It has also been observed that the reconstructed f (R) has satisfied a sufficient condition for a realistic model. In the subsequent phase the reconstructed f (R) is applied to the model of chameleon scalar field and the scalar field f and the potential V(f) are tested for quasi-exponential ex pansion. It has been observed that although the reconstructed f (R) satisfies one of the sufficient conditions for realistic model, the quasi-exponential expansion is not available due to this reconstruction. Finally, the consequences pre-bounce ekpyrotic inflation i n f (R) gravity are compared to the background solution for f (R) matter bounce.