We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

This paper secures the analytical soliton solutions of the perturbed NLSE gives to (1). The existence criteria have been demonstrated and the wave speed of the soliton befall out. To achieve all the results obtained we used the mathematical technique. In view of the results obtained, some new additional one have been reported in left-handed metamaterials.

The standard approach to integrable nonlinear evolution equations (NLEE) usually uses the following steps: 1) Lax representation $[L,M]=0$; 2)~construction of fundamental analytic solutions (FAS); 3) reducing the inverse scattering problem (ISP) to a Riemann-Hilbert problem (RHP) $\xi^+(x,t,\lambda) =\xi^-(x,t,\lambda) G(x,t\lambda)$ on a contour $\Gamma$ with sewing function $G(x,t,\lambda)$; 4) soliton solutions and possible applications.Step 1) involves several assumptions: the choice of the Lie algebra $\mathfrak{g}$ underlying $L$, as well as its dependence on the spectral parameter, typically linear or quadratic in $\lambda$. In the present paper we propose another approach which substantially extends the classes of integrable NLEE.Its first advantage is that one can effectively use any polynomial dependence in both $L$ and $M$. We use the following steps: A) Start with canonically normalized RHP with predefined contour $\Gamma$; B) Specify the $x$ and $t$ dependence of the sewing function defined on $\Gamma$; C) Introduce convenient parametrization for the solutions $ \xi^\pm(x,t,\lambda)$ of the RHP and formulate the Lax pair and the nonlinear evolution equations (NLEE); D) use Zakharov-Shabat dressing method to derive their soliton solutions. This needs correctly taking into account the symmetries of the RHP. E) Define the resolvent of the Lax operator and use it analyze its spectral properties.

The main idea of this paper is to investigate the exact solutions and dynamic properties in optical nanofibers, which is modeled by space-time fractional perturbed nonlinear schr\"odinger equation involving Kerr law nonlinearity with conformal fractional derivative. Firstly, by the complex fractional traveling wave transformation, the traveling wave system of the original equation is obtained, then a conserved quantity, namely the Hamiltonian is constructed, and the qualitative analysis of this system is conducted via this quantity by classifying the equilibrium points. Moreover, the prior estimate of the existence of the soliton and periodic solution is established via the bifurcation method. Furthermore, all exact traveling wave solutions are constructed to illustrate our results explicitly by the complete discrimination system for polynomial method.

The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usually obtained. We connect the produced observational metric to the perturbed Friedmann-Lema\^itre-Robertson-Walker metric in the standard general gauge or what is the so-called 1+3 gauge. We derive the relations between these perturbations of spacetime in the observational coordinates and those perturbations in the standard metric approach, as well as the dynamical equations for the perturbations in observational coordinates. We also calculate the observables in the lightcone gauge and re-derive them in terms of Bardeen potentials to first order. A verification is made of the observables in the perturbed lightcone gauge with those in the standard gauge. The advantage of the method developed is that the observable relations are simpler than in the standard formalism, and they are expressed in terms of the metric components which in principle are measurable. We use the perturbed lightcone gauge in galaxy surveys and the calculations of galaxy number density contrast. The significance of the new gauge is that by considering the null-like light propagations the calculations are much simpler due to the non-consideration of the angular deviations.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

In recent years, there has been an increasing demand for personalized experiences in various domains, including the cultural and educational sectors. Museums, as custodians of art, history, and scientific knowledge, are seeking innovative ways to engage their visitors and provide tailored content that enhances their understanding and appreciation of the exhibits. This article presents ExhibitXplorer, a distributed architecture service that leverages geofencing, artificial intelligence, and microservices to enable personalized content delivery in museums. By combining implicit and explicit segmentation of museum visitors and utilizing the GPT API for content generation, ExhibitXplorer offers a dynamic experience to different visitor segments, including researchers, students, casual visitors, and children. The system utilizes push notifications triggered by visitor location changes, allowing seamless delivery of personalized information both indoors and outdoors. Tests were conducted to evaluate the user experience of visitors to an outdoor ethnographic museum. The results showed that 55% of the test participants were satisfied and 45% very satisfied with the way personalized content was delivered.

A technique devised some years ago permits to study a theory in a regime of strong perturbations. This translate into a gradient expansion that, at the leading order, can recover the BKL solution. We solve exactly the leading order equations in a spherical symmetric case and we show that the 4-velocity in such a case is multiplied by an exponential warp factor when the perturbation is properly applied. This factor is always greater than one. We will give a closed form solution of this factor for a simple case. Some numerical examples are also given.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

OSI model used to be common network model for years. In the case of ad hoc networks with dynamic topology and difficult radio communications conditions, gradual departure is happening from the classical kind of OSI network model with a clear delineation of layers (physical, channel, network, transport, application) to the cross-layer approach. The layers of the network model in ad hoc networks strongly influence each other. Thus, the cross-layer approach can improve the performance of an ad hoc network by jointly developing protocols using interaction and collaborative optimisation of multiple layers. The existing cross-layer methods classification is too complicated, because it’s based on the whole manifold of network model layers combinations, regardless their importance. In this work, we review ad hoc networks cross-layer methods, propose the new useful classification of cross-layer methods, and show future research directions in ad hoc networks cross-layer methods development. The proposed classification can help to simplify the goal-oriented cross-layer protocol development.

Two Iron Age settlements, Tuzusai and Taldy Bulak 2 (ca. 500 BCE to 1 CE), located in Southeastern Kazakhstan on the Talgar alluvial fan north of the Tian Shan range, have yielded a small collection of bone, antler/horn, bronze, and stone artifacts with affinity to nomadic art of the first millennium BCE. Both settlements date within the period of late Saka culture. Two pieces have decorative ornamentations with zoomorphic imagery: a small carved fragment of a with carved images of a wing and an ear and a perforated bone disk with the carving of three birds’ heads. The other artifacts include objects associated with Saka weaponry or nomadic economy such as the two antler/horn psalia (cheek pieces) and a bronze amulet. A carnelian bead will also be described as an imported object. These special finds are found on the occupation floors of mud brick houses and pit houses of settlements, not in grave or burial contexts. The objects are placed in stratigraphic sequence in the settlement sites. Then the method for placing these objects within the chronological framework of “animal-style art” is through comparisons with similar objects found throughout Eurasia—a method used in Soviet and Post-Soviet archaeology. The results show that functional and stylistic elements of the six objects indicate that the Talgar settlements were part of a larger world-system of trade and communication along the early Silk Route(s).

In this paper, the authors consider the influence of the type of power supply and the internal parameters of the DC-DC converter on the stability of the system at constant power load. The stability of the system under consideration is important in the design and development of the power supply system for an autonomous consumer. Such a typical system can be a DC microgrid. In the work, when analyzing the stability of the system, the power source is not considered an ideal voltage source, but the active-inductive nature of the voltage source is taken into account, which is equivalent to using a synchronous machine with permanent magnets. The Rauss-Hurwitz algebraic criterion was used as a criterion for analyzing the stability of the system. This will make it possible to build and analyze the areas and boundaries of the system's stability. As a result, the areas and boundaries of the stability of the system were presented. The general trend towards the behavior of the zone of instability of the system was given. At the same time, dependences describing the boundaries of instability are presented, which are combinations of parameters of the DC-DC converter, beyond which the system becomes unstable. The presented definitions of the instability limits can be used as a corrective device of the control system to ensure the stability of the system in the upper limits of the power consumption.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

Remdesivir (RDV) has garnered much hope for its moderate anti-COVID-19 effects, but its limited amelioration of survival in hospitalized patient causes a huge controversy over the applicability of RDV to COVID-19 treatment. Developing strategies to improve its antivirus efficacy is urgently required. As anticipated, RDV exhibits similar behavior with other nucleotide analogs to disrupt the metabolism of natural endogenous ribonucleotides (RNs) and deoxyribonucleotides (dRNs). Alterations in endogenous RNs and dRNs play a critical role in virus replication as well as other key cellular functions. Thus elucidation of the disturbances of RDV on RNs and dRNs could help to understand its exact mechanism of action. Here, the metabolic profiling determined by liquid chromatography–mass spectrometry method showed a general increase in the abundance of nucleotides and a more than 2-fold increase for specific nucleotides. However, the variation of pyrimidine ribonucleotides was relative slight or even contrary, resulting in obvious imbalance between purine and pyrimidine ribonucleotides, which implied the obstacle of RDV to pyrimidine synthesis and could further block the transcription and replication of viral RNA. Additionally, the extreme disequilibrium between cytidine triphosphate (CTP) and cytidine monophosphate might result from the inhibition of CTP synthase and provide a metabolic target for the treatment of COVID-19 infection. Since nucleotides metabolism pathways are vulnerable to nucleotide analogues and are liable to be the regulation targets, it is promising to enhance the efficacy of RDV through co-administration with CTP synthase inhibitors or de novo pyrimidine synthesis inhibitors to exacerbate the imbalance of nucleotide pools.

Abstract: The aim of this study was to identify and quantify polyphenolic compounds in skin extracts from four Bulgarian grape varieties and compare to those of seed extracts. The values of total phenolic contents (TPC), flavonoids, anthocyanins, procyanidins, ascorbic acid in grape skin extracts were determined. The antioxidant capacities of skin extracts were evaluated by DPPH, ABTS, FRAP and CUPRAC methods. The TPC values of skin extracts were 2-3 times lower than those of seed extracts. The significant difference between total parameters values of individual grape varieties were also found. According to the TPC and antioxidant capacity of skin extracts the different grape varieties were in the following order: Marselan ≥ Pinot Noir ˃ Cabernet Sauvignon ˃ Tamyanka. The individual compounds in the grape skin extracts were determined by RP-HPLC and compared with those of seed extracts. The determined composition of skin extracts was significant different from seed extracts composition. Qualitative and quantitative evaluation of the procyanidins and catechins in the skins were carried out. A correlation between phenolic contents, individual composition and antioxidant capacity of different extracts was found. The studied grape extracts have a potential to be applied as natural antioxidants in the pharmaceutical and food industries.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

Nanoparticles of graphene and carbon nanotubes are attractive materials for improvement of mechanical and barrier properties and functionality of biodegradable polymers for food packaging applications. However, the increase of the manufacture and consumption increases the probability of exposure of human and environment to such nanomaterials, this rising questions about the risks of nanomaterials since they can be toxic. For a risk assessment, it is crucial to know whether airborne nanoparticles of graphene and carbon nanotubes can be released from nanocomposites into the environment at their end-life, or they remain embedded in the matrix. In this work the release of graphene and carbon nanotubes from the poly(lactic) acid nanocomposite films were studied for the scenarios of: (i) biodegradation of matrix polymer at the disposal of wastes; and (ii) combustion and fire of nanocomposite wastes. Thermogravimetric analysis in air atmosphere, TEM, AFM and SEM were used to verify the release of nanoparticles from nanocomposite films. The three factors model was applied for the quantitative and qualitative risk assessment to the release of graphene and carbon nanotubes from nanocomposite wastes for these scenarios. Safety concern is discussed in respect to the existing regulations for nanowastes stream.

Chymotrypsin is an important proteolytic enzyme in human digestion system that cleaves milk proteins, through hydrolysis reaction, which makes it interesting subject to study activity of milk proteases. In this work, we compared detection of chymotrypsin by spectrophotometric, dynamic light scattering (DLS) and quartz crystal microbalance (QCM) methods and determined the limit of chymotrypsin detection (LOD), 0.15 ± 0.01 nM for spectrophotometric, 0.67 ± 0.05 nM for DLS and 1.40 ± 0.30 nM for QCM methods, respectively. We discuss peculiarities and give perspective for implementation of detection methods and note that while the optical detection methods are simple to implement, the QCM method is more robust for sample preparation. We give an overview on methods and instruments for detection of chymotrypsin and other milk proteases.

The purpose of the present study was to develop an experimental model for studying of the intra-articular knee movements depending on the work of the knee joint and applied muscle groups in isometric stretching conditions with different tens. The experimental procedure includes ultrasound examination of a knee joint after isometric stretching of healthy men (n=32). The changes in millimeters of the distances between the femur and tibia were measured with ultrasound sonographer at three stages. The first stage was performed on ten (n=10) healthy men at five different sitting and upright positions. In the second and third experimental model stages the lower limbs loading was on 22 participants. Our hypothesis which was confirmed, was that as a result of increasing extraloads on the participants back (2, 5, 10, 15, 17, 20 kg), a intra-articular decrease in the femur-tibia cartilage surface distance wiil be observed. The accuracy of the created experimental model was improved over its three stages from 30% to 9%. Quantitative model data can help to create a mathematical model for the mechanical effects during deformation of the knee joint bone cartilage, as well as to outlines the some future tasks: increasing loading weights; enlarge participant groups; comparison men and women; healthy and pathology comparison.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

Floating Offshore Wind Turbine (FOWT) is an innovative technology with little industry guidance for its hull design. Various FOWT floaters with different hull shapes claim to support the same turbines. Structural integrity and material expense analyses of different pontoon shapes were conducted, and it was found that some configurations, such as those with every two columns connected by both pontoon and bracing, have advantages over others. However, it is important to note that the choice of pontoon shape should be based on the wave loading conditions the floater will be exposed to. While a T-shaped pontoon provides a cost-effective solution under certain wave loading scenarios, it may not be the best option for all conditions. Specifically, ring pontoon designs with full bracing were found to be necessary for withstanding certain wave loads. Therefore, it is important to consider different Dominant Load Parameters (DLP) and ensure that a FOWT floater can withstand all applicable DLPs. An uneven hexahedral column shape, which combines the best attributes of square and round shapes, is proposed as a better alternative to cylindrical columns. It offers ease of manufacture and reasonably low drag. Bracing is found to be necessary for withstanding the wind turbine’s incurred moment and forces. The conclusion is that platform design should prioritize manufacturing costs and strength over maximizing hydrodynamic performance.

Topological states of matter have attracted significant attention due to their intrinsic wave-guiding and localization capabilities robust against disorders and defects in electronic, photonic, and phononic systems. Despite the above topological features phononic crystals share with their electronic and photonic counterparts, finite-frequency topological states in phononic crystals may not always survive. In this work, we discuss the survivability of topological states in Su-Schrieffer-Heeger models with both local and non-local interactions with larger symmetry perturbation. Although such a discussion is still about ideal mass-spring models, the insights from this study set the expectations in continuum phononic crystals, which can further instruct the applications of phononic crystals for practical purposes.

A cosmological model described by the perturbation metric is proposed, in which space is entrained by matter expanding as a result of the Big Bang. In the absence of an input of external energy and momentum, the solution of the Einstein equations assumes a pressure equal to zero and an accelerated expansion. The cosmological perturbation model explains the difference in measurements of the Hubble constant using gravitational lensing and a distance ladder.

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

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control system with bounded disturbances. First, by constructing an appropriate Lyapunov-Krasovskii functional, we obtained a delay-dependent condition, which determed the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in form of liner matrix inequalities is given to solve the problem of controller design with reachable set estimation. Finally, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to verify the usefulness of our result.

The pentose phosphate pathway (PPP) is one of three major pathways involved in glucose metabolism, regulated by glucose-6-phosphate dehydrogenase (G6PD), controlling NADPH formation. NADPH, in turn, regulates the balance of oxidative stress and reactive oxygen species (ROS) levels. G6PD dysfunction, affecting PPP, is implicated in neurological disorders, including epilepsy. However, PPP's role in epileptogenesis and ROS production during epileptic activity remains unclear. To clarify these points, we conducted electrophysiological and imaging analyses on mouse hippocampal brain slices. Using the specific G6PD inhibitor G6PDi-1, we assessed its effects on mouse hippocampal slices, examining intracellular ROS, glucose/oxygen consumption, and ROS production during synaptic stimulation and in the 4AP epilepsy model. G6PDi-1 increased basal intracellular ROS levels and reduced synaptically induced glucose consumption but had no impact on ROS production from synaptic stimulation. In the 4AP model, G6PDi-1 didn't significantly alter spontaneous seizure frequency or H2O2 release amplitude but increased the frequency and peak amplitude of interictal events. These findings suggest that short-term PPP inhibition has a minimal impact on synaptic circuit activity.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

This paper discusses the preliminary results of archaeological surveys conducted in the Juuku Region of north-central Kyrgyzstan on the south side of Lake Issyk kul. Our goal was to document ancient and contemporary agropastoral systems over a four millenia time period. During the surveys about 350 loci were identified as settlements, burial mounds, graves, single artifact finds, and artifact scatters (ceramic). The areas of Juuku Valley survey included two discrete polygons: Polygon 1, Lower Juuku at 1750 to 1950 m asl in elevation and Polygon 2, Chak Juuku or Upper Eastern Branch Juuku Valley at 2060 to 2100 m asl in elevation. Three radiometric dates and preliminary archaeobotanical studies were conducted at three exposed profile cuts. The methods included here are: (1) pedestrian surveys; (2) use of digital maps (Google Earth, Encarta); (3) placing archaeological loci within known chronological time periods; (4) AMS dating of charcoal samples collected from profile deposits; and (5) preliminary identification of plant remains found from archaeobotanical samples. The results of our research represent the first step toward inventorying and interpreting archaeological data in the Juuku Valley derived from field studies.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.

An extended classification of active RC- and RLC- filters with Sallen-Key architectures, including those created in the last three years, is proposed. This makes it possible to formulate new design directions for an extended family of active RC- and RLC- Sallen-Key filters (PF, LPF, HPF, RF) for the tasks of high-speed and ultra-fast analog-to-digital signal conversion.

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

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

A nonlinear singularly perturbed Cauchy problem with confluent fuchsian singularities is examined. This problem involves coefficients with polynomial dependence in time. A similar initial value problem with logarithmic reliance in time has been investigated by the author in a recent work, for which sets of holomorphic inner and outer solutions were built up and expressed as a Laplace transform with logarithmic kernel. Here, a family of holomorphic inner solutions are constructed by means of exponential transseries expansions containing infinitely many Laplace transforms with special kernel. Furthermore, asymptotic expansions of Gevrey type for these solutions relatively to the perturbation parameter are established.

We consider a family of nonlinear singularly perturbed PDEs whose coefficients involve a logarithmic dependence in time with confluent Fuchsian singularities that unfold an irregular singularity at the origin and rely on a single perturbation parameter. We exhibit two distinguished finite sets of holomorphic solutions, so-called outer and inner solutions, by means of a Laplace transform with special kernel and Fourier integral. We analyze the asymptotic expansions of these solutions relatively to the perturbation parameter and show that they are (at most) of Gevrey order 1 for the first set of solutions and of some Gevrey order that hinges on the unfolding of the irregular singularity for the second.

A new low-pass filter (LPF) circuit with independent adjustment of various, incl. digitally controlled, pole frequency resistors, pole quality factor and transmission coefficient. The proposed low-pass filter is based on the use of the properties of a multi-differential operational amplifier that performs the functions of a signal adder. The peculiarity of the filter is that it has three inputs, with respect to which different transmission coefficients are implemented, incl. inverting (-1) and non-inverting (+1). To check these properties of a low-pass filter in the Micro-Cap environment, computer simulation of a specific circuit was performed on a multi-differential operational amplifier AD 8130. Mathematical expressions are given for the main parameters of the proposed low-pass filter, which allow parametric synthesis of elements of a specific circuit under given restrictions on the used element base.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

This study focuses on the formulation and analysis of a numerical method to compute singularly perturbed functional differential equations (SP-FDEs) involving large mixed shifts. SP-FDEs are a class of differential equations with both shifts and small perturbation parameter. Such equations arise in various scientific fields to model phenomena with memory effects and perturbed dynamics. In this particular study, the considered SP-FDEs involve large negative shift (delay) and large positive shift (advance). Dealing with large mixed shifts in SP-FDEs gives rise to challenges in terms of stability analysis, numerical methods, and convergence of a solution. In this paper, the influence of the large mixed shifts is treated by choosing a uniform mesh discretized in such a way that the term with the shifts lie on the nodal points. Then, using the Numerov’s finite difference method, the continuous problem is transformed into a finite difference scheme and the influence of the perturbation parameter is handled by introducing a fitting factor in the difference scheme. Stability estimate and convergence analysis of the developed scheme are investigated and proved. Numerical experiments are carried out to demonstrate the validity and applicability of the developed scheme. It is shown that the numerical scheme obtained in this work is parameter-robust of second order convergence rate.

In this work, in spite of Milne’s recommendation using the three-point Newton–Cotes open formula (Milne’s rule) as a predictor rule and three-point Newton–Cotes closed formula (Simpson’s rule) as a corrector rule for 4-th differentiable functions with bounded derivatives. There is still a great need to introduce such formulas in other Lp spaces. Often, we need to approximate real integrals under the assumptions of the function involved. Because of that, the aim of this work is to introduce several Lp error estimates for the proposed perturbed Milne’s quadrature rule. Numerical experiments showing that our proposed quadrature rule is better than the classical Milne rule for certain types of functions are provided as well.

A new circuit of a low-pass filter (LPF) is considered, which is switched on at the input of analog-to-digital converters to limit the spectrum of input signals. The peculiarity of the proposed low-pass filter is the independent adjustment of the pole frequency, the quality factor of the pole and the transmission coefficient by different resistors. Computer simulation performed in the Micro-Cap environment confirms these properties of the LPF. The basic mathematical expressions are obtained, which make it possible to carry out the parametric synthesis of the LPF circuit. It is shown that the sensitivity of the LPF transmission coefficient to changes in the parameters of the frequency-setting elements of the circuit is close to zero and depends only on the ratio of the resistances of the two resistors in the feedback circuit.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3-D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport corrected interface and boundary conditions in NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to eliminate the error introduced by pin-wise homogenization. Moreover, several color set models with varying size and configuration are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or only zero order/moment DFs. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size color set models show better prediction in the whole-core calculations. By coupling different color set models DFs can offer the best accuracy at both eigenvalues and power distributions.

This study presents a pre-processing approach adopted for the radar reflectivity data assimilation and results of simulations with the Harmonie numerical weather prediction model. The method shows an improvement of precipitation prediction within the radar location area in both the rain rates and spatial pattern presentation. With the assimilation of radar data, the model simulates larger water content in the middle troposphere within the layer from 1 to 6 km, with major variations at 2.5–3 km; it also reproduces better the mesoscale belt and cell patterns of precipitation fields.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

In this work, the possibility of fabrication magneto-optical ceramics by vacuum sintering of compacts prepared by electrophoretic deposition (EPD) from suspensions of (Ho0.95La0.05)2O3 (HoLa) nanopowders made by self-propagating high-temperature synthesis and (Y0.9La0.1)2O3 (YLa) nanopowders made by laser synthesis was systematically investigated. The processes of the formation of bulk one- and two-layer compacts by the EPD method from non-aqueous suspensions of nanopowders was studied. The use of acetylacetone and polyvinyl butyral (PVB) was shown to make it possible to obtain stable alcohol suspensions of the nanopowders characterized by high zeta potential values (+29…+80 mV) and to carry out a stable EPD process. One-layer compacts were made from the YLa and HoLa nanopowders with a density of 30–43%. It was found out that the introduction of PVB into the suspension leads to a decrease in the mass and thickness of the green bodies deposited, but does not significantly affect their density. A possibility to make two-layers (YLa/HoLa) compacts with a thickness of up to 2.6 mm and a density of up to 46% was demonstrated. Sintering such compacts in a vacuum at a temperature of 1750°C for 10 hours leads to the formation of ceramics with a homogeneous boundary between the YLa/HoLa layers and thickness of the interdiffused ions layer of about 30 μm.

Epidemics are the most common natural phenomena that have occurred throughout the entire history of human society. Depending on the type of disease and the development of the collective immunity that society had acquired by then, the consequences of epidemics were usually very severe. Precisely because of this, the aim of the paper is a scientific description of the way in which the prescribed preventive measures should be applied from the epidemiological, security, economic, legal and other aspects, so that the society, through the mechanisms of the state, can defend and rehabilitate the consequences of an epidemic of an infectious disease. Eliminating the epidemic's impacts is a very difficult issue. In particular, there is an infectious illness epidemic that is spreading uncontrolled throughout society on the one hand. In order to introduce a quarantine that restricts the epidemic's progress and, if the quarantine lasts long enough, to end the epidemic, contact between members of the social group must be broken. On the other side, the cessation of communication between members of a social group also signifies the cessation of all facets of life in that society, including economic ties, education, growth of culture, scientific research, etc.

The development of the automotive industry leads to the improvement of the designs of automatic transmissions and drives and to the development of methods for monitoring and diagnosing their condition. The trend of improving transmissions comes down mainly to the endless improvement of existing designs of CVTs and variators, which inevitably leads to the complication of designs and methods for their control and diagnostics.There is a need to create a fundamentally new simplified gearbox based on the scientific achievements of mechanics. However, the created structures remained inoperable due to the lack of theoretical justification.The adaptive gear variator developed by the author, which has CVT functions, is a mechanism with two degrees of freedom and with an additional constraint of a fundamentally new type, called a force - speed constraint. The force - speed constraint imposes a force restriction on the movement of links, while maintaining the number of degrees of freedom in the kinematics. Monitoring the state of the developed gearbox in the form of a non-switchable gear variator is greatly simplified, since the largest number of faults occur in the control system, and there is no control system in the gear variator. It seems possible to apply the digital twin method to diagnose the developed simplified CVT.The proposed article is devoted to a theoretical description of a fundamentally new adaptive gearbox, created on the basis of the latest achievements in mechanics, with the prospect of developing a simplified monitoring and diagnostic system for it

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

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

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

In a 24-week-long experiment, 31 rats were assigned to one of 3 groups: a Control group receiving standard chow and water, a Fructose group receiving standard chow and a 20% fructose solution, or an STZ+lipids group that received a fat-enriched diet following a single 25 mg/kg streptozotocin injection at the onset of the diet. Both groups experienced significantly increased caloric intake but did not gain weight above the Control group level. Adipocytes in subcutaneous and visceral adipose depots of both groups had smaller size compared to control and higher density in tissue. Respirometric analyses unveiled a substantial increase in mitochondrial respiration across all adipose tissue types in both dietary intervention groups, with greater changes observed in the Fructose group. Correlation analyses demonstrated that in both experimental groups high tissue respiration is associated with better biochemical profile and closer to control adipose tissue morphology. Increased tissue respiration in adipose depots could be an important mechanism of resilience to excessive caloric intake.

Positive invariant set is an important concept of dynamic systems. The purpose of this paper is to study the sufficient and necessary conditions that the set of ellipsoids and the Lorenz cone are positive invariant sets of discrete time systems. By means of nonlinear programming and induced norm, the problem of positive invariance is formulated as an optimization problem, and the equivalent dual form optimization is also presented using the dual optimization method. Our results provide more alternative methods for determining the positive invariance of quadratic form convex sets from the point of view of optimization and dual optimization. The effectiveness of this method is demonstrated by numerical examples.

This comparative study aims to investigate environmental awareness, knowledge, and safety among students in Montenegro and North Macedonia, considering the unique socio-cultural and environmental contexts of both countries. A mixed-methods approach involving surveys and interviews was employed to gather data from students in educational institutions across Montenegro and North Macedonia. The study assessed various factors, including students' awareness of environmental issues, their perceived level of knowledge, and their attitudes towards safety measures. A comprehensive series of 400 face-to-face interviews was carried out and these interviews encompassed 200 students from Montenegro and an equal number from North Macedonia, taking place at two esteemed academic institutions: The University of Montenegro in Podgorica and The University of St. Clement of Ohrid, Bitola, Republic of North Macedonia. Our hypothetical conceptual framework proposes that a combination of variables, including gender (H1), age (H2), year of study (H3), and rate of study (H4), significantly influences the attitudes of students from Montenegro and North Macedonia towards environmental awareness, safety, and knowledge. Research findings indicate significant variations in environmental awareness and knowledge perception among students in the two countries. While both Montenegro and North Macedonia face environmental challenges, differences in educational systems and socio-economic factors contribute to distinct attitudes and behaviors towards environmental issues and safety practices. This study sheds light on the importance of understanding regional differences in environmental awareness and knowledge perception among students. By identifying areas of strength and areas needing improvement, policymakers and educators can develop targeted interventions to enhance environmental education and foster a culture of sustainability in both Montenegro and North Macedonia.

The structural evolution and phase composition of multi-block thermoplastic polyurethanes, with different nature of the soft segments based on poly(butylene adipate) (PBA), were analyzed during in-situ thermal treatments. A combination of synchrotron small- and wide-angle X-ray scattering, differential scanning calorimetry, thermogravimetric analysis, and FTIR spectroscopy was used to determine the influence of macrodiol nature and crystallization conditions on the polymorphic behavior of PBA. Using a new synthesis scheme, a relatively high degree of crystallinity for urethane blocks was achieved, which depends on the diisocyanate type in the structure of the soft segment. The hard segment domains impose geometrical constraints on PBA, thereby altering its crystallization process compared to the neat oligomer. Thus, crystallization after annealing at a low temperature (80 °C) is fast, predominantly yielding a metastable β-phase. When heated to 180 °C, which is higher than the hard-segment melting temperature, a phase-separated structure is observed. Subsequent crystallization is slower, favoring the formation of the stable α-PBA modification. The phase separation can be observed even after the hard block melting. A notably slow crystallization from an isotropic melt was documented after the disruption of phase separation at 230 °C.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Characterized in biomedical terms, stretching exercises have been defined as movements applied by external and/or internal forces – to increase muscle and joint flexibility, decrease muscle stiffness, to elevate joint range of motion (ROM), to increase the length of the morpho-functional unit “muscle-tendon”, to improve joint, muscle and tendon movements, contraction and relaxa-tion. The present review examines and summarizes the initial and recent literature data related to the biomechanical, physiological and therapeutic effects of static stretching (SS) on flexibility and other physiological characteristics of the main structural and functional unit “joint-ligaments-tendon-muscle”. The healing and therapeutic effects of SS, soon combined with other rehabilitation techniques (massage, foam rolling – with and without vibrations; hot/cold therapy, etc.) are discussed in relationship to creation of individual (patient-specific) or group programs for treatment and prevention of joint injuries as well as for improving performance in sports. From a theoretical point of view, the role of SS as positively affecting the composition of the connective tissue matrix is pointed out: type I-III collagen synthesis, hyaluronic acid and glucosaminoglycans (GAGs) turnover – under influence of the transforming growth factor beta-1 (TGF-β-1). Different variables as collagen type, biochemistry, elongation and elasticity are used as molecular biomarkers. Recent studies evaluated that the static progressive stretching therapy could prevent/reduce the development of arthrogenic contractures, joint capsule fibrosis, muscle stiffness and need new clinical applications. Combined stretch techniques are proposed and ap-plied in medicine and sports, depending on their long- and short-term effects on variables such as ROM, EMG activity, muscle stiffness, etc. The results obtained are of theoretical and practical interest for development of new experimental, mathematical and computational models and creation of efficient therapeutic programs. The healing SS effects on the main structural and functional unit – “joint-ligament-tendon-muscle” need further investigations, which could clarify and evaluate benefits of SS in prophylaxis and treatment of joint injuries - in healthy and ill in-dividuals, in older adults, as compared to young, active and well-trained persons, as well as to professional athletes.

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

Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .

The deregulated markets have replaced the traditional way of trading electricity from the producers to the consumer, via government-owned organizations and regulated tariffs. Nowadays, electricity prices are determined by the offer-demand mechanism and consumers can negotiate tariffs with their supplier of choice. For classic wholesale suppliers, the tariffs are a result of the transactions performed on the wholesale market and the energy mix available in certain geographical regions. In parallel with becoming eligible and participating in retail electricity markets, the consumers use increasingly local generation sources based mostly on renewable energy technologies such as PV panels, and become prosumers. They want to be able to sell back to the market the generation surplus, in order to obtain the maximum benefits from their initial investment. Currently, several trading mechanisms for prosumers are available, ranging from the simplest, selling back the surplus to an aggregator at fixed tariffs, to more complex market schemes. This paper proposed a two-tier local market model for prosumers and consumers connected in microgrids, based on the blockchain technologies and other technologies and concepts such as remote sensing, smart grids, crowdsourcing and energy poverty.

The deregulated markets have replaced the traditional way of trading electricity from the producers to the consumer, via government-owned organizations and regulated tariffs. Nowadays, electricity prices are determined by the offer-demand mechanism and consumers can negotiate tariffs with their supplier of choice. For classic wholesale suppliers, the tariffs are a result of the transactions performed on the wholesale market and the energy mix available in certain geographical regions. In parallel with becoming eligible and participating in retail electricity markets, the consumers use increasingly local generation sources based mostly on renewable energy technologies such as PV panels, and become prosumers. They want to be able to sell back to the market the generation surplus, in order to obtain the maximum benefits from their initial investment. Currently, several trading mechanisms for prosumers are available, ranging from the simplest, selling back the surplus to an aggregator at fixed tariffs, to more complex market schemes. This paper proposed a two-tier local market model for prosumers and consumers connected in microgrids, based on the blockchain technologies and other technologies and concepts such as remote sensing, smart grids, crowdsourcing and energy poverty.

Emerging of mass-spectroscopy with inductively-coupled plasma (ICP-MS) made possible to study the microelement composition of crude oil and its derivatives (with the limit of detection at the ppt level). We have studied the crude oil composition of some West Siberian and Tatarstan oilfields with the ICP-MS method to detect 50 rare, rare-earth, and other microelements. The elemental composition is reasonably comparable to their concentrations in ultrabasites whereas the contents of most of the elements are low to the limit. On the diagrams of rare-earth elements, one can see the prevalence of light lanthanides and positive europium anomaly. The study shows that crude oils have a specific microelement composition that stands out from other geological systems.

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

The gravel road pavement has a lower construction cost but poorer performance than the asphalt surface. It also emits dust and deforms under the impact of vehicle loads and ambient air factors. The resulting ripples and ruts are constantly deepening, increasing vehicle vibrations and fuel consumption, reducing safe driving speed and comfort. In this article, existing pavement quality evaluation indexes are analysed, and a methodology for their adaptation for roads with gravel pavement is proposed. This article reports the measured wave depth and length of the gravel pavement profile by the straightedge method of a 160 m long road section in three road exploitation stages. The measured pavement elevation was processed according to ISO 8608, and vehicle frequency response has been investigated using simulations in MATLAB/Simulink. The applied International Roughness Index (IRI) analysis showed that a speed of 30-45 km/h instead of 80 km/h provides the objective results of IRI calculation on the flexible pavement due to a decreasing velocity of vehicle's unsprung mass on a more deteriorated road pavement state. The influence of the corrugation phenomenon of gravel pavement has been explored, identifying specific driving safety and comfort cases. Finally, an increase in the Dynamic Load Coefficient (DLC) at a low speed of 30 km/h on the most deteriorated pavement and a high speed of 90 km/h on the middle-quality pavement demonstrates the demand for timely gravel pavement maintenance and the complicated prediction of a safe driving speed for drivers.

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

This research work deals with the formulation of numerical scheme with algorithm to compute singularly perturbed partial differential equations(SP-PDEs) involving a significant negative shift. The problem involves small parameter which causes a rapidly changing boundary layers in the vicinity of a body, and the negative shift term causes interior layer. Such appearance of an abruptly varying layers causes difficulties to find the exact solution and it is not adequate to employ classical numerical methods. The technique presented in this research work simplifies these challenges and yields accurate numerical solution.The stability and convergence analyses of the methods are examined and proven. To test the developed technique, numerical experiments are carried out and confirmed with theoretical analysis.

Background: Despite the fact that bone reconstructive surgeries are widely practiced worldwide, the search for an ideal bone replacement matetrial is still an open issue. We aimed to provide an overview of the current status of research and developments in this field with a focus on sapphire materials; Methods: A literature search and review was conducted using the PubMed, Scopus, and Embase databases. We searched for literature using the following keywords: bone implants; biocompatible materials; bone replacement material; sapphire implants; Results: Sapphire has a unique combination of mechanical, physical and chemical characteristics thanks to wich it has an excelent biocompatability and biointegrity.Unlike other materials it is incredibly strong and has a high endurance. The successful experience of using this material in medical instrument engineering, dentistry and cardiac surgery shows its benefits; Conclusions: We consider that sapphire is a perspective material for bone replacement implants and researchers should look in this direction.

We offered the circuit of a discrete analog filter (DAF) low frequencies of second-order on switchable capacitors, which differs from the known ones in that three capacitors with one terminal are connected to a common bus, and the frequency of the DAF pole depends not only on the ratio of the capacitances of the frequency-setting capacitors, but also on the ratio of resistances two additional resistors in the feedback. This allows at constant values ​​of the capacitances and a fixed switching frequency of electronic switches, control the pole frequency by changing the resistance ratio of additional resistors. Computer simulation of the developed circuit was performed in the Micro-Cap environment. It has been established that the DAF has a transmission coefficient close to minus one at very low frequencies and a transmission coefficient close to zero at higher frequencies.

Transmission electron microscopy methods were used to analyze the cementite substructure in the head of special-purpose long rails of DT400IK category made of hypereutectoid steel after long-term operation on an experimental track on the Russian Railways ring (the passed tonnage is 187 million tonnes). It is noted that the study of various aspects of cementite – its structure, morphology, chemical composition, crystal lattice defects is relevant. The steel structure is represented by three morphological components at a distance of 10 mm from the sample surface: lamellar perlite, fractured and fragmented perlite. The volume fraction of lamellar perlite in the material is 65%. It is shown that after operation, the cementite plates are bent and separated by ferrite bridges. In the plates of ferrite and cementite, a dislocation substructure is formed which is of chaotically distributed and network type in ferrite and of ordered type in cementite. An increased density of dislocations at ferrite-cementite interfaces compared to the volume of ferrite plates was noted. Two possible mechanisms of deformation transformation of lamellar perlite grains are indicated: fracture of cementite plates and carbon pulling out from the lattice of the carbide phase. It is indicated that in the dissolution of cementite plates, the interfacial boundaries “α-phase-cementite” play an important role. The removal of carbon from cementite plates occurs most intensively near defects in ferrite and cementite. The formed nanosized particles of tertiary cementite are unevenly distributed in the ferrite plates, most of them are observed at the locations of ferrite subgrains and interfacial boundaries. This results in non-uniform diffraction contrast in dark-field images of cementite plates. Nanosized particles of cementite can be taken out into the interlamellar space of pearlite colonies in the process of dislocation slip, or they are formed as a result of deformation decomposition, which is less likely. Fragmentation of ferrite and cementite plates is revealed and azimuthal components of total misorientation angles are estimated. The mechanisms of mass transfer of carbon atoms over interstitial sites, deformation vacancies, dislocation tubes, grain boundaries and fragments are considered. According to all the established patterns of the cementite substructure transformation, a comparison with the results for rails made of hypoeutectoid steel was performed.

Grid refinement is used to save computing costs while preserving high precision of fluid simulation. In the Lattice Boltzmann Method, grid refinement often uses interpolated values. We found a method, where interpolation in space and time is not required. For this purpose, we used the moment matching condition and rescaling the non-equilibrium part of populations, and developed the recalibration procedure that allows to transfer information between different LBM stencils in the simulation domain. Then, we build non-uniform lattice which uses stencils with different shapes on the transition. The resulting procedure is verified on the 2D Poisselle flow and the advected vortex benchmark. In prospect, grids with adaptive geometry can be built with the use of the proposed method.

The interaction of human immunodeficiency virus with human cells is responsible for all stages of the viral life cycle, from the infection of CD4+ cells to reverse transcription, integration, and the assembly of new viral particles. To date, a large amount of OMICs data as well as information from functional genomics screenings regarding the HIV-1-host interaction has been accumulated in the literature and in public databases. We processed databases containing HIV-host interactions and found 2910 HIV-1-human protein-protein interactions, mostly related to viral group M subtype B, 137 interactions between human and HIV-1 coding and non-coding RNAs, essential for viral lifecycle and cell defense mechanisms, 232 transcriptomics, 27 proteomics, and 34 epigenomics HIV-related experiments. Numerous studies regarding network-based analysis of corresponding OMICs data have been published in recent years. We overview various types of molecular networks, which can be created using OMICs data, including HIV-human protein-protein interaction networks, co-expression networks, gene regulatory and signaling networks, and approaches for the analysis of their topology and dynamics. The network-based analysis can be used to determine the critical pathways and key proteins involved in the HIV life cycle, cellular and immune responses to infection, viral escape from host defense mechanisms, and mechanisms mediating different susceptibility of humans to infection. The proteins and pathways identified in these studies may represent a basis for developing new anti-HIV therapeutic strategies such as new small-molecule drugs preventing infection of CD4+ cells and viral replication, effective vaccines, "shock and kill" and "block and lock" approaches to cure latent infection.

This paper discusses approaches to the numerical integration of the coupled nonlinear Schrödinger equations system in case of few-mode wave propagation. The wave propagation assumes the propagation of up to nine modes of light in an optical fiber. In this case, the light propagation is described by the non-linear coupled Schrödinger equation system, where propagation of each mode is described by own Schrödinger equation with other modes interactions. In this case, the non-linear coupled Schrödinger equation system solving becomes increasingly complex, because each mode affects the propagation of other modes. The suggested solution is based on the direct numerical integration approach, which is based on a finite-difference integration scheme. The well-known explicit finite-difference integration scheme approach fails, due to the non-stability of the computing scheme. Due to this fact, the combined explicit/implicit finite-difference integration scheme, based on the implicit Crank–Nicolson finite-difference scheme, is used. It allows ensuring the stability of the computing scheme. Moreover, this approach allows separating the whole equation system on the independent equation system for each wave mode at each integration step. Additionally, the algorithm of numerical solution refining at each step and the integration method with automatic integration step selection are used. The suggested approach has performance gains (or resolutions) up to three or more orders of magnitude in comparison with the split-step Fourier method due to the fact that there is no need to produce direct and inverse Fourier transforms at each integration step. The main advantage of the proposed method is the ability to calculate the propagation of an arbitrary number of modes in the fiber.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

We still do not have satisfactory answers about the inflationary and accelerating expansions of the universe, the missing mass problem, and the origins of the four fundamental forces and the quantum phenomena. Here, we introduce a new model of matter and space and a postulate on a constant of motion, and then show that an equation of motion derived from the constant of motion could provide new understandings of the above problems. For example, we show that there is a natural inflation scenario and that the co-moving distance to the closest accelerating supernova is clearly given as $c/(\sqrt{3} H)$ ($\sim$8.1 billion ly). In addition, we show that, in a system including a proton and an electron, the equation of motion has eight acceleration terms, some of which are suspected to be responsible for the four fundamental forces and the galaxy rotation anomaly. From further discussion, we conjecture that in order to understand the gravitational and strong interactions and the quantum phenomena, it is necessary to consider the expansion of the universe. The lensing mass distribution is explained, based on another postulate on a method of representing superposition.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

Four-wire low voltage microgrids supply one-phase consumers with continuously changing electricity demand. For addressing climate change concerns, governments implemented incentive schemes for residential consumers, encouraging the installation of home PV panels for covering self-consumption needs. In the absence of sufficient storage capacities, the surplus is sold back by these entities, called prosumers, to the grid operator or in local markets, to other consumers. While these initiatives encourage the proliferation of green energy resources, and ample research is dedicated to local market designs for prosumer-consumer trading, the main concern of distribution network operators is the influence of power flows generated by prosumer surplus injection on the operating states of microgrids. The change in power flow amount and direction can greatly influence the economic and technical operating conditions of radial grids. This paper proposes a metaheuristic algorithm for prosumer surplus management that optimizes the power surplus injections using the automated control of three-phase inverters, with the aim of improving the active power losses and balancing the phase voltage profiles. A case study is performed on two real distribution networks with distinct layouts and load profiles and the algorithm shows its efficiency in both scenarios.

A growing number of households benefit from the government subsidies to install renewable generation facilities such as PV panels, used to gain independence from the grid and provide cheap energy. In the Romanian electricity market, these prosumers can sell their generation surplus only at regulated prices, back to the grid. A way to increase the number of prosumers is to allow them to make higher profit by selling this surplus back into the local network. This would also be an advantage for the consumers, who could pay less for electricity exempt from network tariffs and benefitting from lower prices resulting from the competition between prosumers. One way of enabling this type of trade is to use peer-to-peer contracts traded in local markets, run at microgrid (μG) level. This paper presents a new trading platform based on smart peer-to-peer (P2P) contracts for prosumers energy surplus trading in a real local microgrid. Several trading scenarios are proposed, which give the possibility to perform trading based on participants’ locations, instantaneous active power demand, maximum daily energy demand and the principle of first come first served implemented in an anonymous blockchain trading ledger. The developed scheme is tested on a low-voltage (LV) microgrid model to check its feasibility of deployment in a real network. A comparative analysis between the proposed scenarios, regarding traded quatities and financial benefits is performed.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, impulse spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. At the end of the paper the question on a possibility of second quantization of the electron field in the spinor coordinate space is touch upon. The statement that the electron and positron have the same, and exactly positive energy, and have opposite signs of charge and opposite signs of mass is also justified. Accordingly, in the process of annihilation their total energy, momentum, charge and mass do not change. It is shown that if we take as an axiom the conservation at interaction of the total mass of the system of particles taking into account its sign, then it is possible to explain the difference between bosons and fermions in the statistics to which they obey.

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

The aim this text to present the confined covariant quark model (CCQM) and review its applications to the decays of B mesons. We do so in the context of existing experimental measurements and theoretical results of other authors, which we review also. The physics principles are in detail exposed for the CCQM, the other results (theoretical and experimental) are surveyed in an enumerative way with comments. We proceed by considering successively three categories of decay processes: leptonic, semileptonic and non-leptonic.

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations converting the defined Lax pairs to some simpler forms and reducing the variety of the Lax pairs this way are found. The direct method and its possible applications to other types of evolution equations are discussed.

Hyperandrogenism and insulin resistance are co-pathologies of polycystic ovary syndrome (PCOS). Recent evidence has suggested that elevated local cortisol levels are associated with ovarian and endometrial insulin resistance in hyperandrogenic PCOS patients, but the molecular mechanisms underlying these clinical findings remain unclear. We and others have used chronic treatment with human chorionic gonadotropin (hCG) and insulin to create an in vivo rodent model for the onset and development of PCOS-like phenotypes. Here, we aimed to determine whether the molecular mechanisms of glucocorticoid receptor (GR) signaling, mitochondrial function, and local inflammation in the ovary and uterus are intrinsically different in PCOS-like rats compared to controls. In both the ovary and the uterus, decreased expression of two GR protein isoforms was concurrent with increased expression of Fkbp51 but not Fkbp52 mRNA in PCOS-like rats compared to controls. However, PCOS-like rats exhibited an opposite regulation of Hsd11b1 or Hsd11b2 mRNAs in the two tissues. Further, the expression of several oxidative phosphorylation-related protein components was decreased in the PCOS-like ovary and uterus, but surprisingly the expression of many genes involved in mitochondrial function and homeostasis was increased in the same tissues and animals. Additionally, PCOS-like rats showed the increased expression of ovarian and uterine NFκB signaling proteins and Tnfaip3 mRNA. In PCOS-like rats, while similar decreased expression of Il1b, Il6, and Mmp2 mRNAs was seen in the ovary and uterus, the opposite regulation of Tnfa, Ccl2, Ccl5, and Mmp3 mRNA expression was observed in the two tissues. Both ovaries and uteri from PCOS-like animals showed increased collagen deposition compared to controls. Collectively, our observations suggest that hyperandrogenism and insulin resistance disrupt ovarian and uterine GR activation and trigger compensatory or adaptive effects for mitochondrial homeostasis, allowing tissue-level maintenance of mitochondrial function in order to limit ovarian and uterine dysfunction. Our study also suggests that hyperandrogenism and insulin resistance-induced activation of NFκB signaling resulting in aberrant regulation of inflammation-related gene expression might be tissue specific in female reproductive tissues.

Bottlebrush (BB) elastomers with water-soluble side chains and tissue-mimetic mechanical properties are promising for biomedical applications like tissue implants and drug depots. This work investigates the microstructure and phase transitions of BB elastomers with crystallizable polyethylene oxide (PEO) side chains by real-time synchrotron X-ray scattering. In the melt, the elastomers exhibit the characteristic BB peak corresponding to the backbone-to-backbone correlation. Upon crystallization of the side chains, the intensity of the peak decays linearly with crystallinity, and eventually vanishes due to BB packing disordering within intercrystalline amorphous gaps. This behavior of the bottlebrush peak differs from an earlier study of BBs with poly(ε-caprolactone) side chains, explained by stronger backbone confinement in the case of PEO, a high-crystallinity polymer. Microstructural models based on 1D SAXS correlation function analysis suggest crystalline lamellae of PEO side chains separated by amorphous gaps of monolayer-like BB backbones.

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

We employ hierarchy of models (HoM) with 2, 3 and 4 parameters to reanalyze the nucleation kinetics in the electrodeposition as quantified by n(t) - “the number of nuclei vs. time” data obtained at different overvoltages from precise experiments on electrodeposition of Hg on two different types of Pt-cathodes by Ivan V. Markov and Evgenia Stoycheva [1]. The obtained two scales, nmax and , are used to rescale the original data mapping it on a master curve in coordinates . Our main result is obtained by studying further the dependence of these two scales on the overvoltage (analogue of supersaturation). Surprisingly, for one of the two cathode types - the “hemispherical single-crystal electrode” (as defined by the authors), there is discontinuity in the “ vs. overvoltage” dependence – an almost horizontal jump from 85 to 86 mV accompanied by a change in the slope of the dependence - it is ~ -1 and ~ -0.5 after. For the other cathode - “plane structureless platinum electrode”,  decreases smoothly. Combined, these two behaviors point at the so called “cusp catastrophe”. We compare our findings with published results on protein nucleation.

Papain-like protease PLpro, a domain within a large polyfunctional protein nsp3, plays key roles in the life cycle of SARS-CoV-2, being responsible for the first events of cleavage of a polyprotein into individual proteins (nsp1-4) as well as for the suppression of cellular immunity. Here, we developed a new genetically encoded fluorescent sensor, named PLpro-ERNuc, for detection of PLpro activity in living cells using translocation-based readout. The sensor was designed as follows. A fragment of nsp3 protein was used to direct the sensor on the cytoplasmic surface of endoplasmic reticulum (ER) membrane, thus closely mimicking the natural target of PLpro. The fluorescent part included two bright fluorescent proteins - red mScarlet I and green mNeonGreen, separated by a linker with the PLpro cleavage site. Nuclear localization signal (NLS) was attached to ensure accumulation of mNeonGreen into the nucleus upon cleavage. We tested PLpro-ERNuc in the model of recombinant PLpro expressed in HeLa cells. The sensor demonstrated expected cytoplasmic reticular network in the red and green channels in the absence of protease, and efficient translocation of the green signal into nuclei in the PLpro-expressing cells (14-fold increase of the nucleus/cytoplasm ratio). Then, we used PLpro-ERNuc in the model of Huh7.5 cells infected with SARS-CoV-2 virus, where it showed robust ER-to-nucleus translocation of the green signal in the infected cells 24 h post infection. We believe that PLpro-ERNuc represents a useful tool for screening PLpro inhibitors as well as for monitoring virus spread in a culture.

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind soil erosion and common soil erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. The main objective of this paper is to estimate the best exponent of the MUSLE, and to estimate the best combination of the exponent and topographic factor of the MUSLE under hydro-climatic conditions of Ethiopia. For the sake of calibration procedure, the main parameters of the MUSLE which directly affect soil erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which have no any physical meaning (i.e coefficient a and exponent b) are estimated through calibration. It is verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e approximately 100\%). For the best combination of the exponent and topographic factor, the performance of the MUSLE is greater than or equal to 80\% for all four watersheds under our consideration, we expect the same for other watersheds of Ethiopia.

The main goal of this paper is to present results of preliminary archaeological research on the south side of Lake Issyk-Kul in Kyrgyzstan. We test the hypothesis that agropastoral land use changed over four millennia from the Bronze Age through the ethnographic Kirghiz period due to economic, socio-political, and religious changes in the prehistoric and historic societies of this region. Our research objectives are to: (1) describe and analyze survey results from Lower Kizil Suu Valley; (2) discuss the results of radiometric and archaeobotanical samples taken from three stratigraphic profiles from three settlements from the Juuku Valley, including these chronological periods: the Wusun period (200 to 400 CE), the Qarakhanid period (1100 to 1200 CE), and the ethnographic Kirghiz period (1700 to 1900 CE); and (3) conduct preliminary GIS spatial analyses on the Iron Age mortuary remains (Saka and Wusun period). This research emerges out of the first archaeological surveys conducted in 2019 - 2021 and includes the Lower Kizil Suu alluvial fan; it is an initial step toward developing a model for agropastoral land use for upland valleys of the Inner Tian Shan Mountains.

This paper presents the perturbation theory for the double–sine–Gordon equation. We obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution.. In the particular case λ = 0 we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ=-1/8, we derive a phase-locked solution with the same frequency of the linear case. In general we obtain both coherent (solitary waves, lumps and so on) solutions as well as fractal solutions. We can demonstrate the existence of envelope wobbling solitary waves, because of the phase modulation depending on the solution amplitude and on the position. The main conclusion is that it is too reductive focus only on coherent solutions for the double sine-Gordon equation, because of the very rich behavior for the DSG nonlinear equation, including wobbling chaotic and fractal solutions.