Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser algebraic topology is fixed. Should the spacetime we reside in takes up one of the more exotic choices, and there is no obvious reason why it shouldn't, apparent pathologies would inevitably plague calculus-based physical theories assuming the standard vanilla structure, due to the non-existence of a diffeomorphism and the consequent lack of a suitable portal through which to transfer the complete information regarding the exotic physical dynamics into the vanilla theories. An obvious plausible consequence of this deficiency would be the uncertainty permeating our attempted description of the microscopic world. We tentatively argue here, that a re-inspection of the key ingredients of the phenomenological particle models, from the perspective of exotica, could possibly yield interesting insights. Our short and rudimentary discussion is qualitative and speculative, because the necessary mathematical tools have only just began to be developed.

The application of evolutionary optimization algorithms in problem solving is currently gaining wide popularity. Use of Differential Evolution (DE) algorithm in obtaining analytically approximate solution of unstable second order initial value Ordinary Differential Equation (ODE) is presented in this work. The methodology involves solving an associated problem of optimization with con-strains to get an analytically approximate solution for the ODE under consider-ation. Three test cases were used to demonstrate the efficiency of our method. In comparison with other methods discussed in the literature, our method gave significant improvement on the accuracy of the obtained results.

In this article, we consider the three dimensional $\alpha$-fractional nonlinear delay differential system of the form \begin{align*} D^{\alpha}\left(u(t)\right)&=p(t)g\left(v(\sigma(t))\right),\\D^{\alpha}\left(v(t)\right)&=-q(t)h\left(w(t))\right),\\D^{\alpha}\left(w(t)\right)&=r(t)f\left(u(\tau(t))\right),~ t \geq t_0, \end{align*} where $0 < \alpha \leq 1$, $D^{\alpha}$ denotes the Katugampola fractional derivative of order $\alpha$. We have established some new oscillation criteria of solutions of differential system by using generalized Riccati transformation and inequality technique. The obtained results are illustrated with suitable examples.

This research presents a solution to the problem of planning the optimum area for economic crops by developed mathematical models and developed an algorithm to solve the problem of planning the optimum area by considered economic value for the maximize profit of farmers. The data were collected from farmers in 8 provinces in the northeastern region of Thailand. The 3 economic crops studied were rice, cassava and sugarcane. The solving problem methods were 1) Created mathematical models and solved the problems with Lingo V.11. 2) Improved Differential Evolution algorithms (I-DE) to solve the problems, which had 3 local search methods included (Swap, Cyclic Move and K-variable moves). The results of this study showed that in the small and medium problems instances, Lingo V.11 and DE provided equal profit outcome but DE was faster but in the large size of test instances DE generated better solution than that of Lingo v.11 when Lingo simulation time is set to 250 hours and DE simulation time has set to maximum 21.82 minutes. 2) Comparing DE and I-DE , I-DE outperforms DE in finding the better solution for all size of test instances (small, medium and large).

In this paper, we investigate a new subclass of univalent functions defined by a generalized differential operator, and obtain some interesting properties of functions belonging to the class R^m λµ ( α, β, γ, υ ).

In this paper, we employ fuzzy Sumudu transform for solving system of linear fuzzy differential equations with fuzzy constant coefficients. The system with fuzzy constant coefficients is interpreted under strongly generalized differentiability. For this purpose, new procedures for solving the system are proposed. A numerical example is carried out for solving system adapted from fuzzy radioactive decay model. Conclusion is drawn in the last section and some potential research directions are given.

In this paper, we established the existence of PC-mild solutions for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained by using the techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we have used the distributed characteristic operators to define the mild solution of the system. Results obtained here improve and extend some known results.

Calculus, as a starting point to everyone's study of mathematics, was developed along with classical mechanics. Though not rigorously formulated, the intuition for differential form and infinitesimal motion makes calculus not hard to understand. And hence it does not require great effort to grasp the principles of classical mechanics. However, the situation becomes quite different when it comes to the quantum world. Given a particle system, what of interest is always the physical quantity of this system, such as energy, position, momentum, entropy, etc. But it is no longer straightforward.

Molecular studies regarding regulatory elements such as small ncRNAs and their mechanisms are poorly understood in infectious diseases. Tuberculosis is one of the oldest infectious diseases of humanity, and it is still a challenge to prevent and treat it. The control of the infection as well as its diagnosis are still complex, and treatments used are linked to several side effects. This study aimed to investigate miRNA’s expression profile to identify possible biomarkers for tuberculosis. We applied NGS techniques to investigate miRNA’s global expression profile from blood samples of infected patients with tuberculosis, their respective healthy physicians, and external healthy individuals as controls. Samples from 22 individuals run through a differential expression, target genes, gene set enrichment, and miRNA-gene network analysis. We observed 153 altered miRNAs, among which, only three DEmiRNAs (hsa-let-7g-5p, hsa-miR-486-3p and hsa-miR-4732-5p) were found between the investigated patients and their respective physicians. These DEmiRNAs are suggested to play an important role in granuloma regulation and their immune physiopathology. Our results propose that miRNAs may be involved in immune modulation, regulating the repertoire of genes expressed in the immune system’s cells. Our findings encourage the application of miRNAs as potential biomarkers for tuberculosis.

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

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 propose a notion of $(q,\sigma,\tau)$-differential graded algebra, which generalizes the notions of $(\sigma,\tau)$-differential graded algebra and $q$-differential graded algebra. We construct two examples of $(q,\sigma,\tau)$-differential graded algebra, where the first one is constructed by means of generalized Clifford algebra with two generators (reduced quantum plane), where we use a $(\sigma,\tau)$-twisted graded $q$-commutator. In order to construct the second example, we introduce a notion of $(\sigma,\tau)$-pre-cosimplicial algebra.

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.

This study aims to implement a SSDBI (single-stage differential boost inverter, SSDBI) applying in a single-stage BESS (battery energy storage system, BESS) topology, which can supply power from lower voltage battery module to AC load. Compared with the common two-stage topology, which has a two-stage converter and higher voltage battery module array, the single-stage topology can reduce the number of cells and components, and improve the power density. In addition, a modified SPWM control was proposed to reduce the control complexity of the SSDBI while improving the THD of the inverter. The modified SPWM control can reduce the duty ratio of the SSDBI and the stress on the components to improve the AC voltage output waveform and reduce the THD value about 2.654%.

Image segmentation and classification still represent an active area of research since no universal solution can be identified. Established segmentation algorithms like thresholding are problem specific, treat well the easy cases and mostly relied on single parameter i.e intensity. Machine learning approaches offer alternatives where predefined features are combined into different classifiers. On the other hand, the outcome of machine learning is only as good as the underlying feature space. Differential geometry can substantially improve the outcome of machine learning since it can enrich the underlying feature space with new geometrical objects, called invariants. In this way, the geometrical features form a high-dimensional feature space for each pixel, where original objects can be resolved. Alternatives based on the geometry of the image scale-invariant interest points have been exploited successfully in the field of computer vision. Here, we integrate geometrical feature extraction based on signal processing, machine learning, and input relying on domain knowledge. The approach is exemplified on the ISBI 2012 image segmentation challenge data set. As a second application, we demonstrate powerful image classification functionality based on the same principles, which was applied to the HeLa and HEp-2 data sets. Obtained results demonstrate that feature space enrichment properly balanced with feature selection functionality can achieve performance comparable to deep learning approaches.

Background: Traditional omic analysis relies on p-value and fold change as selection criteria. There is an ongoing debate on their effectiveness in delivering systemic and robust interpretation, due to their dependence on assumptions of conformity with various parametric distributions.Here, we propose a threshold-free selection method based on robust, non-parametric statistics, ensuring independence from the statistical distribution properties and broad applicability. Such methods could adapt to different initial data distributions, contrary to statistical techniques based on fixed thresholds. Methods: Our work extends the Rank Products methodology with a neutral selection method of high information-extraction capacity. We introduce the calculation of the RP distribution’s entropy to isolate the features of interest by their contribution to the distribution’s information content. The aim is a methodology performing threshold-free identification of the differentially expressed features, which are highly informative about the phenomenon under scrutiny. Conclusions: Applying the proposed method on microarray (transcriptomic and DNA methylation) and RNAseq count data of varying sizes and noise presence, we observe robust convergence for the different parameterisations to stable cutoff points. Functional analysis through BioInfoMiner and EnrichR was used to evaluate the information potency of the resulting feature lists. Overall, the derived functional terms provide a systemic description highly compatible with the results of traditional statistical hypothesis testing techniques. The methodology behaves consistently across different data types. The feature lists are compact and information-rich, indicating phenotypic aspects specific to the tissue and biological phenomenon i nvestigated. Selection by information content measures efficiently addresses problems, emerging from arbitrary thresholding, thus facilitating the full automation of the analysis.

An easier method for the calibration of differential drive robots is presented. Most of the calibration is done on-board and it is not necessary to expend too much time taking note of the robot's position. The calibration method does not need a big free space to perform the tests. The bigger space is just in a straight line, which is easy to find. Results with the proposed method are compared with those from UMB as a reference, and they show very little deviation while the proposed calibration is much simpler.

In this paper, we investigate some kind of Dynkin game under $g$-expectation induced by backward stochastic differential equation (shortly for BSDE). We define the lower and upper value functions $\underline{V}_t=ess\sup\limits_{\tau\in{\mathcal{T}_t}} ess\inf\limits_{\sigma\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$ and $\overline{V}_t=ess\inf\limits_{\sigma\in{\mathcal{T}_t}}ess\sup\limits_{\tau\in{\mathcal{T}_t}}\mathcal{E}^g_t[R(\tau,\sigma)]$, respectively. Under some regular assumptions, a pair of saddle point is obtained and the value function of Dynkin game $V(t)=\underline{V}_t=\overline{V}_t$ follows. Furthermore, the constrained case of Dynkin game is also considered.

Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image analysis, directional statistics and probability theory. Exact analytic designs and solutions are known in the 2D case, where they have been obtained using Fourier transform on $SE(2)$. Here we extend these approaches to 3D using Fourier transform on the Lie group $SE(3)$ of rigid body motions. More precisely, we define the homogeneous space of 3D positions and orientations $\mathbb{R}^{3}\rtimes S^{2}:=SE(3)/(\{\mathbf{0}\} \times SO(2))$ as the quotient in $SE(3)$. In our construction, two group elements are equivalent if they are equal up to a rotation around the reference axis. On this quotient we design a specific Fourier transform. We apply this Fourier transform to derive new exact solutions to Fokker-Planck PDEs of $\alpha$-stable Lévy processes on $\mathbb{R}^{3}\rtimes S^{2}$. This reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions. We compare the exact probability kernel for $\alpha = 1$ (the diffusion kernel) to the kernel for $\alpha=\frac12$ (the Poisson kernel). We set up SDEs for the Lévy processes on the quotient and derive corresponding Monte-Carlo methods. We verify that the exact probability kernels arise as the limit of the Monte-Carlo approximations.

We present a differentially private extension of the block coordinate descent based on objective perturbation. The algorithm iteratively performs linear regression in a federated setting on vertically partitioned data. In addition to a privacy guarantee, the algorithm also offers a utility guarantee; a tolerance parameter indicates how much the differentially private regression may deviate from an analysis without differential privacy. The algorithm’s performance is compared with the standard block coordinate descent algorithm and the trade-off between utility and privacy is studied. The performance is studied using both artificial test data and the forest fires data set. We find that the algorithm is fast and able to generate practical predictions with single-digit privacy budgets, albeit with some accuracy loss.

Alfalfa, an important legume forage, is an ideal crop for sustainable agriculture and a potential bioenergy plant. Drought, one of the most common environmental stresses, substantially affects plants’ growth, development and productivity. MicroRNAs (miRNAs) are newly discovered gene expression regulators that have been linked to several plant stress responses. To elucidate the role of miRNAs in drought stress regulation of alfalfa, a high-throughput sequencing approach was used to analyze 12 small RNA libraries comprising of 4 samples, each with 3 biological replicates. We identified 348 known miRNAs, belonging to 80 miRNA families, from the 12 libraries and 281 novel miRNAs using Mireap software. 18 known miRNAs in roots and 12 known miRNAs in leaves were screened out as drought-responsive miRNAs. Except for miR319d and miR157a which were upregulated under drought stress, the expression pattern of drought-responsive miRNAs were different between roots and leaves in alfalfa. This is the first study discovering miR157a, miR1507, miR3512, miR3630, miR5213, miR5294, miR5368 and miR6173 are drought-responsive miRNAs. Target transcripts of drought-responsive miRNAs were computationally predicted. All 447 target genes for the known miRNAs were predicted using an online tool. This study provides a significant insight on understanding drought-responsive mechanisms of alfalfa.

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.

In this present paper, we deal with the generalized (k, s)-fractional integral and differential operators recently defined by Nisar et al. and obtain some generalized (k, s)-fractional integral and differential formulas involving the class of a function as its kernels. Also, we investigate a certain number of their consequences containing the said function in their kernels.

A wide variety of renal neoplasms can have cystic areas. It happens for different reasons: some tumors have an intrinsic cystic architecture, others have a pseudocystic degeneration of necrotic foci or they have cystically dilated renal tubules constrained by stromal neoplastic cells. Clear cell renal cell carcinoma (CCRCC), either solid or cystic, is the most frequent type of renal cancer. While pseudocysts are found in high-grade aggressive CCRCC, cystic growth is associated to low-grade indolent cases. The latter also form through a cyst-dependent molecular pathway and they are more frequent in patients suffering from VHL disease. The differential diagnosis with multilocular cystic renal neoplasm of low malignant potential and clear cell papillary renal cell tumor can be especially hard and it requires a focused macroscopical and microscopical pathological analysis. As every class of renal tumors include cystic forms, a knowledge of criteria for a differential diagnosis is mandatory.

Polynomial recurrence bounds for a class of stochastic differential equations with a gradient type drift and an additive Wiener process are studied without Lyapunov functions.

Hessenberg differential algebraic equations (Hessenberg-DAEs) with high index play a critical role in the modeling of mechanical systems and multibody dynamics. Motivated by the widely used Lie Group Differential Algebraic Equation (LGDAE) method which only handles index 2 systems, we propose a Modified Extended Lie Group Differential Algebraic Equation (MELGDAE) method for solving index 3 Hessenberg-DAEs, and provide theoretical analysis to deepen the foundation of the MELGDAE method.The performance of the MELGDAE method is compared with the standard methods RADAU and MEBDF on index 2 and 3 DAE systems, and it is demonstrated that the MELGDAE integrator exhibits competitive performance in terms of high accuracy and the preservation of algebraic constraints. In particular, all differential variables in index 3 Hessenberg DAEs achieve second-order convergence using the MELGDAE method, which suggests potential for extension to Hessenberg-DAEs with an index of 4 or higher.

The study is devoted to the issues of mathematical modeling and simulating the sport differential mechanism (DM) with controllable torque redistribution. The issue is caused by the elaboration of ADAS systems with the automated torque vectoring for transmissions of all-wheel-drive (AWD) vehicles and the inclusion of such devices in the combined autonomous vehicle trajectory control scheme. At the article's beginning, the use of devices for redistributing traction forces is reasoned by analyzing the curvilinear vehicle motion, where they could ensure the accuracy of vehicle steerability. The literature review highlights modern developments in the field of modeling and researching such DMs. Considering the vehicle turn with a minimum radius, the conditions corresponding to passing greater torque over the outrunning rear axle are determined. All the mechanism's components and loads acting between them are described in detail. To form an original method of mathematical description of the mechanism functioning, the system of differential equations, systems of kinematic and force connections are considered separately. The article details the mathematical approach to generalize the way for automating the equation compilation for rotational mechanical systems such as vehicle transmissions. In the simulation section, a Simulink model reflecting the functional components and calculation procedures is presented. A series of testing and simulations on the DM operation with forcible torque distribution is carried out. Modeling data are presented, and the analysis of simulation results is performed. In the completion, conclusions are made regarding the scope and use of this model and the prospects for further developing the method proposed to automate the formation of equation systems.

Studies on the prevalence of Autism Spectrum Disorders show a gender disproportion. In the last years, there has been an increasing interest in the search for an explanation. There are two main lines of research; the first one looks for sex-related biological reasons that justifies the low prevalence of ASD in women (some protective factor related to hormones or immune system among others), and the second line of studies is related to the possible biases introduced in the diagnostic tools or procedures. In this article, a review of the latter line of research is made. Theoretical analysis following two objectives: a) Analysis of possible biases in diagnostic tools and b) Other non-biological explanations for gender differences in the prevalence of ASD. The literature analyzed provides contradictory results although it evidences the possible bias both in the construction of the diagnostic tools and in the assessment and determination of their standards. It is necessary to develop specific or complementary tools and diagnostic procedures differentiated by gender in order to control for this bias.

The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by backpropagating errors through the ODE solver, the neural network weights are adjusted accordingly to minimize the difference between the predicted and actual ODE solutions. It is shown that even when the dimensionality of the thermochemical manifold is trimmed to remove redundant species, the proposed approach accurately captures the correct physical behavior and reproduces the results obtained using the full chemical kinetic mechanism.

Rubbish in a forest environment is a great threat to this ecosystem, but this threat may also apply to the lost benefits for visitors to the forest. Previous studies proved that forest areas have a positive effect on obtaining psychological relaxation in the people visiting them. However, it was not known whether this restorative experience could be disturbed in any way by the presence of an open dump in the forest. To check how the presence of a landfill affects the visitors, an experiment was planned in which the respondents observed a forest area with a landfill and a forest landscape without a landfill for 15 minutes (control). The respondents then assessed the landscape using the semantic differential method and the Perceived Restorativeness Scale (PRS). An analysis of these observations showed that the presence of a landfill in the forest significantly changed the appreciation of the landscape by the respondents, the values of positive experiences decreased, and the negative experiences increased. Restorativeness was also reduced. Based on the results, it can be concluded that the presence of garbage in the forest may interrupt the restorative experience of its visitors.

A new generation of universal tools and languages for modeling and simulation multi-physical domain applications emerged and became widely accepted, which generate large-scale systems of differential algebraic equations (DAEs) automatically. Motivated by the characteristics of DAEs systems with large dimension, high index or block structures, we first propose a modified Pantelides’ algorithm (MPA) for any high order DAEs based on its Σ matrix, which is similar to Pryce’s Σ method. By introducing a vital parameter vector, a modified Pantelides’ algorithm with parameter has been presented.It leads to a block Pantelides’ algorithm (BPA) naturally which can immediately compute the crucial canonical offsets for whole (coupled) systems with block-triangular form. We illustrate these algorithms by some examples. And numerical experiments show that the time complexity of BPA can be reduced by at least O(ℓ) compared to the MPA, which is mainly consistent with the results of our analysis.

The overwhelming majority of bladder cancers are transitional cell carcinomas. Albeit mostly monotonous, carcinomas in the bladder may occasionally display a broad spectrum of histological features that should be recognized by pathologists because some of them represent a diagnostic problem and/or lead prognostic implications. Sometimes these features are focal in the context of conventional transitional cell carcinomas, but some others are generalized across the tumor making its recognition a challenge. For practical purposes, the review distributes the morphologic spectrum of changes in architectural and cytological. So, nested and large nested, micropapillary, myxoid stroma, small tubules and adenoma nephrogenic-like, microcystic, verrucous, and diffuse lymphoepithelioma-like, on one hand, and plasmacytoid, signet ring, basaloid-squamous, yolk-sac, trophoblastic, rhabdoid, lipid/lipoblastic, giant, clear, eosinophilic (oncocytoid), and sarcomatoid, on the other, are revisited. Key histological and immunohistochemical features useful in the differential diagnosis are mentioned. In selected cases, molecular data associated with the diagnosis, prognosis, and/or treatment are also included.

A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.

Type-2 fuzzy sets were introduced by L. Zadeh aiming at modelling some settings in which fuzzy sets (usually called type-1 fuzzy sets) are not sufficient to reflect certain uncertainty degrees - loosely speaking, they are fuzzy sets whose membership degrees are ordinary fuzzy sets. On the other hand, fiber bundles are topological entities of extreme importance in Mathematics itself and many other scientific areas, like Physics (General Relativity, Field Theory etc.), finance modelling, and statistical inference. The present work introduces a conceptual link between the two ideas and conjectures about the potential mutual benefits that can be obtained from this viewpoint.As an objective and usable product of the presented ideas, it is described a framework for defining type-2 fuzzy hedges, proper to operate on interval type-2 fuzzy sets.

Because only two variables are needed to characterize a simple thermodynamic system in equilibrium, any such system is constrained on a 2D manifold. Of particular interest are the exact 1-forms on the cotangent space of that manifold, since the integral of exact 1-forms is path-independent, a crucial property satisfied by state variables such as internal energy dE and entropy dS. Our prior work [1] shows that given an appropriate language of vector calculus, a machine can re-discover the Maxwell equations and the incompressible Navier-Stokes equations from data. In this paper, We enhance this language by including differential forms and show that machines can re-discover the equation for entropy dS given data. Since entropy appears in various fields of science in different guises, a potential extension of this work is to use the machinery developed in this paper to let machines discover the expressions for entropy from data in fields other than classical thermodynamics.

In this paper, we investigate an analytical solution of a class of nonlinear fractional integro-differential equation base on a generalized fractional power series expansion. The fractional derivatives are described in the conformable's type. The new approach is a modified form of the well-known Taylor series expansion. The illustrative examples are presented to demonstrate the accuracy and effectiveness of the proposed method

Kelly's Criterion is well known among gamblers and investors as a method for maximizing the returns one would expect to observe over long periods of betting or investing. These ideas are conspicuously absent from portfolio optimization problems in the financial and automation literature. This paper will show how Kelly's Criterion can be incorporated into standard portfolio optimization models. The model developed here combines risk and return into a single objective function by incorporating a risk parameter. This model is then solved for a portfolio of 10 stocks from a major stock exchange using a differential evolution algorithm. Monte Carlo calculations are used to verify the accuracy of the results obtained from differential evolution. The results show that evolutionary algorithms can be successfully applied to solve a portfolio optimization problem where returns are calculated by applying Kelly's Criterion to each of the assets in the portfolio.

For a system that turns out to be inactive in time t, the past entropy is considered as an uncertainty measure for the past lifetime distribution. In this study, we consider a coherent system that includes n components and has the property that all the components of the system have failed at time t. To assess the predictability of the coherent system’s lifetime, we use the system’s signature to determine the Rényi entropy of its past lifetime. We study several analytical results, including expressions, bounds, and order properties for this measure.

We study the existence of positive solutions for a system of Hadamard fractional differential equations on an infinite interval with nonnegative nonlinearities, subject to coupled nonlocal boundary conditions which contain Hadamard fractional derivatives and Riemann-Stieltjes integrals. In the proof of the main results, we use the Guo-Krasnosel'skii fixed point theorem and the Leggett-Williams fixed point theorem.

Variable during practice is widely accepted to be advantageous for motor learning and therefor a valuable strategy to effectively reduce high-risk landing mechanics and prevent primary anterior cruciate ligament (ACL) injury. Few attempts have examined the specific effects of variable train-ing in athletes who have undergone ACL reconstruction. Thereby it is still unclear to what extent the variations in different sensor areas lead to different effects. Accordingly, we compared the effects of versatile movement variations (DL) with variations of movements with emphasis on disrupting visual information (VMT) in athletes who had undergone ACL reconstruction. For-ty-five interceptive sports athletes after ACL reconstruction were randomly allocated to a DL group (n= 15), VT group (n= 15) or control group (n= 15). The primary outcome was functional performance (Triple Hop Test). The secondary outcomes included dynamic balance (Star Excur-sion Balance Test (SEBT)), biomechanics during single-leg drop-landing task hip flexion (HF), knee flexion (KF), ankle dorsiflexion (AD), knee valgus (KV), and vertical ground reaction force (VGRF), and kinesiophobia (Tampa Scale of Kinesiophobia (TSK)) assessed before and after the 8-weeks of interventions. Data were analyzed be means of 3×2 repeated measures ANOVA fol-lowed by post hoc comparison (Bonferroni) at the significance level of p≤0.05. Significant group × time interaction effects, main effect of time and main effect of group were found for triple hop test, all eight directions of SEBT, HF, KF, AD, KV, VGRF and TSK. There was no significant main ef-fect of group in HF and triple hop test. Also, significant differences in triple hop test, seven direc-tions of SEBT, HF, KF, KV, VGRF and TSK were found between control group with the DL and VMT groups. Between group differences in AD and medial direction of SEBT were not signifi-cant. Also, there was no significant differences between VMT and control groups in triple hop test and HF variables. Both motor learning (DL and VMT) programs improved outcomes in patients after ACL reconstruction. Findings suggest that DL and VMT training programs lead to compa-rable improvements in rehabilitation.

Bismuth oxides are well-known electro-catalysts in fuel cells systems; they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of BiO₂ and MnO₂ as catalysts in the pharmaceutical analysis is analytical method for the determination of heavy metal antibacterial agents in Pharmaceutical Dosage form is developed. The method is based on the voltammetric determination of heavy metal using Bidified platinum electrode by Bismuth oxide. The two components are oxidized at the Bidified electrode surface with the development of current that is linearly proportional to their concentrations in the range of 7.04*10^-7- 1*10^-3 M heavy metal. The oxidation reaction of the two components is pH-dependent, in which the buffer used is Britton-Robinson at pH = 7.00 where maximum peak current and maximum peak separation is obtained. The regression factors obtained from the calibration curves are 0.9812. The method of analysis was validated, where the limit of detection (LOD) and the limit of quantitation (LOQ) were calculated to be 1.44*10^-4 M, 4.36*10^-4 M and 1.27*10^-4 M, 3.84*10^-4 M respectively, the percentage recovery of both components was also calculated to 77 % for heavy metal.

Standard cell culture is routinely performed at supraphysiological oxygen concentrations (~18% O2). Conversely, oxygen levels in most tissues range from 1%–6% (physioxia). Such hyperoxic conditions can alter reactive oxygen species (ROS) production, energy metabolism, mitochondrial network dynamics, and response to drugs and hormones. The aim of this project was to investigate the transcriptional response to different oxygen levels and whether it is similar across cell lines, or cell-line specific. Using RNA-seq, we performed differential gene expression and functional enrichment analyses in four human cancer cell lines, LNCaP, Huh-7, PC-3, and SH-SY5Y cultured at either 5% or 18% oxygen for 14 days. We found that oxygen levels affected transcript abundance of hundreds of genes, with the affected genes having little overlap between cell lines. Functional enrichment analysis also revealed different processes and pathways being affected in each cell line. Interestingly, we found that the top differentially expressed genes are involved in cancer biology. Further, we observed several hypoxia-inducible factor (HIF) targets upregulated at 5% oxygen, suggesting a role of HIF at physiological oxygen conditions. Finally, oxygen strongly induced transcription of mitochondrial genes in most cell lines, in a cell-type specific manner too. We conclude that cellular response to oxygen is widely cell-type specific, emphasizing the importance of maintaining physioxia in cell culture.

Background: The reliability of a recent review of meningiomas in the archeologic record was difficult to assess, given the inverted sex ratio of the report and other contents apparently at variance with anatomical/medical findings in scientifically-identified cases. It therefore seemed appropriate to reexamine the nature of meningiomas and derive improve criteria for their recognition in the archeologic record and distinguish them from hemangiomas and bone marrow hyperplasia (recognized in the form of porotic hyperostosis). Methods: Medically-documented cases of meningiomas, hemangiomas and cranial bone marrow hyperplasia were examined to establish a macroscopic standard that distinguishing among them. Alleged cases in the archeologic record were examined for conformity with those criteria. Results: An en face pattern of uniform mesh with contained whorls appears pathognomonic for meningiomas. This contrasts with the non-uniform marrow expansion displacement of trabeculae in porotic hyperostosis and non-uniform vascular displacement of trabeculae in hemangiomas. Reassessment of past attributions revealed few cases of meningiomas that could be confidently diagnosed. Those identified has sex ratios parsimonious with medical literature reports. Conclusions: Criteria suggested for identifying meningiomas permits distinguishing from hemangiomas, bone marrow hyperplasia (porotic hyperostosis) and from the macroscopically-observable surface spicules characteristic of osteosarcomas. Examination for fulfillment of criteria for meningiomas and hemangiomas seems to provide a picture (including sex ratios) more parsimonious with the clinical literature, concluding that Cook and Danforth’s disparate ratios were related to less fastidious case selection. Additionally, confidence in recognizing porotic hyperostosis may be compromised because of apparent similar macroscopic alterations to those seen with hemangiomas.

Physicists have employed various approaches to solve the “paradox” and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin “paradox” is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

Conventionally, partial differential equations (PDE) problems are solved numerically through discretization process by using finite difference approximations. The algebraic systems generated by this process are then finalized by using an iterative method. Recently, scientists invented a short cut approach, without discretization process, to solve the PDE problems, namely by using machine learning (ML). This is potential to make scientific machine learning as a new sub-field of research. Thus, given the interest in developing ML for solving PDEs, it makes an abundance of an easy-to-use methods that allows researchers to quickly set up and solve problems. In this review paper, we discussed at least three methods for solving high dimensional of PDEs, namely PyDEns, NeuroDiffEq, and Nangs, which are all based on artificial neural networks (ANNs). ANN is one of the methods under ML which proven to be a universal estimator function. Comparison of numerical results presented in solving the classical PDEs such as heat, wave, and Poisson equations, to look at the accuracy and efficiency of the methods. The results showed that the NeuroDiffEq and Nangs algorithms performed better to solve higher dimensional of PDEs than the PyDEns.

Molybdenum oxides is well-known electro-catalysts in fuel cells systems, they are usually used as anodic materials for the oxidation of low molecular weight alcohols. The utilization of Mo as catalysts in the pharmaceutical analysis is not common yet. In this study, bare glassy carbon electrodes were modified by the oxides by means of electrochemical deposition and the modified electrodes were used as catalysts for the electrochemical oxidation of hydrochlorothiazide (HCT). Well-resolved anodic peaks were reported for the analyzed pharmaceuticals when the Mo/GCE was utilized for the analysis of HCT. Analytical performance of the modified electrodes was evaluated based on the following statistical parameters; linearity ranges, correlation coefficients, limits of detection and quantitation, and recovery values. The prepared electrodes were used for the determination of the active ingredients in their pharmaceutical formulations and the reported activity was correlated to influence of the utilized pH on both structures of the used electrodes and the detected analytes.

A mathematical expression to describe cation absorption of root is expressed with simulation results. The root cells selectively emit H+ ions with active transport consuming ATPs to establish electrical gradient. The gradient promotes external positive ions to flow into the roots, while carries negatively charged particles with symport. In this paper, a mathematical model whose independent variables are the concentrations of external and internal cation is presented. This differential equation is induced from Ohm’s law. The equation has terms for plant physiology, ion’s physical and electrical properties, growth of plant, and interaction between the root and the surroundings. Simulation showed that the physiology-related coefficient has important role on nutrition absorption.

In the context of the French-German space lidar mission MERLIN dedicated to the determination of the atmospheric methane content, an end-to-end mission simulator is being developed. In order to check whether the instrument design meets the performance requirements, simulations have to count all the sources of noise on the measurements like the optical energy variability induced by speckle. Speckle is due to interference as the lidar beam are quasi monochromatic. Speckle contribution to the error budget has to be estimated but also simulated. In this paper, the speckle theory is revisited and applied to MERLIN double pulsed IPDA lidar and also to the DLR demonstrator CHARM-F. Results show: on the signal path, speckle noise depends mainly on the size of the illuminating area on ground; on the solar flux, speckle is fully negligible both because the pixel size and the optical filter spectral width; on energy monitoring path a decorrelation mechanism is needed to reduce speckle noise on averaged data. Speckle noises for MERLIN and CHARM-F can be simulated by Gaussian noises with only one random draw by shot separately for energy monitoring and signal paths.

In this paper we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, we analyze the analytical solution for a class of fractional models associated with Logistic model, Von Foerster model and Bertalanffy model is presented graphically for various fractional orders and solution of corresponding classical model is recovered as a particular case.

The present paper introduces a method of basis transformation of vector fields that is specifically applicable to polynomials space and differential equations with certain polynomials solutions such as Hermite, Laguerre and Legendre polynomials. The method based on separated transformation of vector space basis by a set of operators that are equivalent to the formal basis transformation and connected to it by linear combination with projection operators. Applying the Forbenius covariants yields a general method that incorporates the Rodrigues formula as a special case in polynomial space. Using the Lie algebra modules, specifically , on polynomial space results in isomorphic algebras whose Cartan sub-algebras are Hermite, Laguerre and Legendre differential operators. Commutation relations of these algebras and Baker-Campbell-Hausdorff formula gives new formulas for special polynomials

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.

The dynamics of the main photosynthetic structures is studied by mathematical modeling methods in this article. Chlorophyll portion variability in phytoplankton and the formation of energy-intensive substances in the process of photosynthesis underlie the models. These cellular components are considered in terms of their participation in the growth of specific biomass. Computational experiments are presented that simulate various degrees of environmental friendliness. The corresponding functions are built in accordance with seasonal fluctuations throughout the year in the Far East region of Russia. The stability of model solutions in long-term dynamics is also investigated. The models were tested for biological adequacy and their effectiveness was compared. For the model selected as a result of the comparison, the optimal control problem has been formulated and solved. It is shown that in this way it is possible to reduce the space of the initial components of the model system.

This paper describes methods for evaluating the thermal properties of textile materials, clothing composites, and clothing using an integrated measurement system that includes a hot plate, a multi-purpose differential conductometer, a thermal manikin, a temperature gradient measurement device, and a device for measuring the physiological parameters of the human body during the exact evaluation of garment thermal comfort. In practice, measurements were taken on four types of materials widely used in the production of conventional and protective clothing. The measurements were carried out using a hot plate and a multi-purpose differential conductometer, determining the thermal resistances of the material in its uncompressed form and a force that was ten times greater than that needed to determine its thickness. Using a hot plate and a multi-purpose differential conductometer, thermal resistances of textile materials were assessed at different levels of material compression. On hot plates, both conduction and convection had an impact on thermal resistance, but in multi-purpose differential conductometer, only conduction did. Moreover, the reduction of thermal resistance was observed while compressing textile materials.

We study the Gaudin models with gl(1|1) symmetry that are twisted by a diagonal matrix and defined on tensor products of polynomial evaluation gl(1|1)[t]-modules, extending all the results of to the twisted case. Namely, we give an explicit description of the algebra of Hamiltonians (Gaudin Hamiltonians) acting on tensor products of polynomial evaluation gl(1|1)[t]-modules and show that there exists a bijection between common eigenvectors (up to proportionality) of the algebra of Hamiltonians and monic divisors of an explicit polynomial written in terms of the highest weights and evaluation parameters. In particular, our result implies that each common eigenspace of the algebra of Hamiltonians has dimension one. We also give dimensions of the generalized eigenspaces.

Systems genetics is key for integrating a large number of variants associated with diseases. Vitamin K (VK) is one of the scarcely studied conditions in lieu of ascertaining either the differentially expressed genes (DEGs) or variants in an individual subpopulation of diseased phenotypes associated with VK, viz. myocardial infarction, renal failure, prostate cancer, thrombosis, thrombocytopenia, coagulation related diseases to name a few. In this work, we have screened characteristic DEGs common to three VK-related diseases, viz. myocardial infarction, renal failure and prostate cancer and asked whether or not any DEGs in addition to pathogenic variants are common to these conditions. We attempt to bridge the gap in finding characteristic biomarkers and discuss the role of long noncoding RNAs (lncRNAs) in the biogenesis of VK deficiencies.

Schizophrenia (SCZ) is a severe mental disorder that may result in hallucinations, delusions, and extremely disordered thinking. How each cell type in the brain contributes to SCZ occurrence is still unclear. Here, we leveraged the human dorsolateral prefrontal cortex bulk RNA-seq data, then used the RNA-seq deconvolution algorithm CIBERSORTx to generate SCZ brain single-cell RNA-seq data for a comprehensive analysis to understand SCZ-associated brain cell types and gene expression changes. Firstly, we observed that the proportions of brain cell types in SCZ differed from normal samples. Among these cell types, astrocyte, pericyte, and PAX6 cells were found to have a higher proportion in SCZ patients (astrocyte: SCZ = 0.163, Control = 0.145, P.adj = 4.9×10-4; pericyte: SCZ = 0.057, Control = 0.066, P.adj = 1.1×10-4; PAX6 : SCZ = 0.014, Control = 0.011, P.adj = 0.014), while the L5/6_IT_CAR3 cells and LAMP5 cells are the exact opposite (L5/6_IT_Car3 : SCZ = 0.102, Control = 0.108, P.adj = 0.016; LAMP5 : SCZ = 0.057, Control = 0.066, P.adj = 2.2×10-6). Next, we investigated gene expression in cell types and functional pathways in SCZ. We observed chemical synaptic transmission dysregulation in two types of GABAergic neurons (PVALB and LAMP5), and immune reaction involvement in GABAergic neurons (SST) and non-neuronal cell types (endothelial and oligodendrocyte). Furthermore, we observed that some differential expression genes from bulk RNA-seq displayed cell-type-specific abnormal in the expression of molecules in SCZ. Finally, the cell types with the SCZ-related transcriptomic changes could be considered to belong to the same module since we observed two major similar coordinated transcriptomic changes across these cell types. Together, our results offer novel insights into cellular heterogeneity and the molecular mechanisms underlying SCZ.

In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.

The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection (a(t)) and recovery (u(t)) rates regulating the transitions from the susceptible to the infected and from the infected to the recovered compartment, respectively. Here approximated SIR-solutions for different time dependencies of the infection and recovery rates are derived which are based on the adiabatic approximation assuming time-dependent ratios k(t)=u(t)/a(t) varying slowly in comparison to the typical time characteristics of the pandemic wave. For such slow variations the available analytical approximations from the KSSIR-model, valid for a stationary value of the ratio k, are used to insert a-posteriori the adopted time-dependent ratio of the two rates. Instead of investigating endless different combinations of the time dependencies of the two rates a(t) and u(t) a suitably parameterized reduced time dependence of the ratio k(tau) is adopted. Together with the definition of the reduced time this parameterized ratio k(tau) allows us to cover a great variety of different time dependencies of the infection and recovery rates. The agreement between the solutions from the adiabatic approximation in its four different studied variants and the exact numerical solutions of the SIR-equations is remarkably good providing strong confidence in the accuracy of the proposed adiabatic approximation.

We enhance Frobenius' method for solving linear ordinary differential equations about regular singular points. Key to Frobenius' approach is the exploration of the derivative with respect to a single parameter; this parameter is introduced through the powers of generalized power series. Extending this approach, we discover that tandem recurrence relations can be derived. These relations render coefficients for series occurring in logarithmic solutions. The method applies to the, practically important, exceptional cases in which the roots of the indicial equation are equal, or differ by a non-zero integer. We demonstrate the method on Bessel's equation and derive previously unknown tandem recurrence relations for coefficients of solutions of the second kind, for Bessel equations of all integer and half-integer order.

In this study, we consider delta fractional Sturm--Liouville (DFSL) initial value problems in the sense of delta Caputo and delta Riemann-Liouville (R--L) operators. One of the properties of delta fractional difference operators which makes it different from nabla counterpart is to shift its domain. This feature makes it more complex than the nabla fractional operator. We obtain sum representation of solutions for DFSL initial value problems with the help of $\mathcal{Z}-$ transformation. Moreover, we get analytical solutions of homogeneous DFSL problem within Riemann-Liouville (R--L) and Caputo sense, discrete Sturm--Liouville (DSL) problem, continuous fractional Sturm--Liouville (FSL) problem in the sense of R--L and Caputo operators, and continuous Sturm--Liouville (SL) differential problem. From this point of view, we compare all the solutions with each other. Consequently, we show that all results for these four eigenvalue problems are compatible with each other and approach to each other while the orders tends to one, i.e. $\Delta^{\mu }\left( \Delta x\left( t-\mu \right) \right)\cong D_{0^{+}}^{\mu }\left( x^{\prime }\left( t\right) \right)\cong \Delta^2x(n-1) \cong x^{\prime \prime }\left( t\right) =\lambda x\left( t\right),\ \mu\rightarrow1 $ . We support our results comparatively by tables and simulations in detail.

A theoretical model to translate the evolution over time, in early stages, of growth and accumulation of biofilm bacterial mass is introduced. The model implies the solution of a system of differential-difference master equations. The application of an algorithm like Miller´s tree term recurrence, already known for Bessel functions of first kind, allows an exact calculation of the solutions of such equations, for a wide range of parameters values and time. For biofilm model a five term recurrence is deduced and applied in a backwards computation. A suitable normalisation condition completes the reach of the solution.

New class of conserved quantities is constructed. These quantities find direct application in mechanics of dissipative (generally non-conservative) dynamical systems. Approach demands formulation in the language of geometric mechanics, providing theoretical framework for situations with energy flow in and out of the system. As a by product, we suggest possibility of existence of Hamiltonian form for every autonomous ODE system, evolution of which is governed by non-potential generator of motion. Various examples are provided, ranging from physics and mathematics, to chemical kinetics and population dynamics in biology. Applications of these ideas in geometric integration techniques (GNI) of numerical analysis are discussed, and as an example of such, new discrete gradient-based numerical method is introduced.

This paper investigates a range of popular differential evolution (DE) configurations to identify components responsible for emergence of structural bias – a recently identified tendency of algorithms to prefer some regions of search space over others, for reasons unrelated to objective function values. Previous work has explored this tendency for genetic algorithms (GA) and particle swarm optimisation (PSO), finding a relationship between population size and extent of structural bias, hence highlighting potential weaknesses of those algorithms. In current article, we focus on DE, extend the investigation to include consideration of an algorithmic component that is often overlooked – constraint handling mechanism. Towards this end, a wide range of DE configurations was tested here. Results suggest that DE is generally robust to structural bias. Unlike the case with GA and PSO, population size seems to have no influence on DE structural bias. Only one of variants studied – DE/current-to-best/1/bin – shows clear signs of bias, however, we show that this effect is mitigated by a judicious choice of constraint handling technique. These findings contribute towards explaining widespread success of DE variants in algorithm comparison studies; its robustness to structural bias represents the absence of a factor that may confound other algorithms.

The differential gear train and speed regulating motor constitute the variable ratio transmission for grid-connected wind turbine with differential speed regulation. The synchronous generator in the system can accessing the power grid without frequency converter. The transmission can realize the mode of variable speed constant frequency that the wind rotor speed is varying and the generator rotor speed is constant. The power control method is studied under the different wind speed which is lower or higher than rated wind speed with using the relational expression of utilization rate of wind energy Cp, pitch angle β and the tip speed ratio λ. The SIMULINK software is used to build the 1500 kW wind turbine model with differential speed regulation. Some different wind speed is made as input. The feasibility of power control method for grid-connected wind turbine with differential speed regulation is verified by the comparison between the simulation results and the theoretical value of the key parameters.

In this work, a mixture of Elzaki transform and projected differential transform method is applied to solve a nonlinear wave-like equations with variable coefficients. Nonlinear terms can be easily manipulated by using the projected differential transformation method. The method gives the results show that the proposed method is very efficient, simple and can be applied to other applications.

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

The main objective of the present study was to investigate arsenate [As (V)] resistance genes in rice cultivars grown in arsenic contaminated Egyptian soil in order to genetically induce resistance against arsenic in the local rice varieties as well as defining contaminated rice grains and/or soil. Three local rice cultivars; Sakha 102-104 were cultivated on modified Murashige and Skoog Basal Medium (MS medium) containing elevated concentrations of arsenate (0.1, 1 and 10 mg/l). The three varieties showed different resistant attitudes against arsenate with Sakha 104 being the most resistant. Extracted messenger RNA (mRNA) from treated and untreated Sakha 104 plantlets was scanned using differential display to demonstrate the arsenate resistant genes using three different arbitrary primers. About 100 different RNAs with (1500 bp - 50 bp) were obtained from which seven were up-regulated genes, subjected to DNA cloning using TOPO TA system and the selected clones were sequenced. The sequence analysis described four genes out of the seven namely disease resistance protein RPM1, Epstein-Barr virus EBNA-1-like, CwfJ family protein and outer membrane lipoprotein OmlA while the other three genes were hypothetical proteins. It is concluded the four induced genes in the resistant rice cultivar considered as a direct response to arsenic soil pollution. Genes detected in the present study can be used as geno-sensors for rice grains and soil contamination with As (V). Moreover, local rice cultivars may be genetically modified with such genes to induce high resistance and to overcome arsenic soil pollution.

In the note, the authors find several simple and explicit forms for a family of inhomogeneous linear ordinary differential equations studied in "D. Lim, Differential equations for Daehee polynomials and their applications, J. Nonlinear Sci. Appl. 10 (2017), no. 4, 1303-1315; Available online at http://dx.doi.org/10.22436/jnsa.010.04.02".

Recently, there has been a growing interest in the production of electricity from renewable energy sources (RES). The RES investment is characterized by uncertainty, which is long-term, costly, depend on feed-in-tariff and support schemes. In this paper, we address the real option valuation (ROV) of a solar power plant investment. The real option framework is investigated. This framework considers the renewable certificate price, furthermore the cost of delay between establishing and operating the solar power plant. The optimal time of launching the project and assess the value of deferred option are discussed. The new three stage numerical methods are constructed, the Lobatto3C-Milstein (L3CM) methods. The numerical methods are integrated with concept of Black-Scholes option pricing theory, and applied in option valuation for solar energy investment with uncertainty. The numerical results of L3CM, finite difference and Monte Carlo methods are compared to show the efficiency of our methods. Our data set refers to the Arab Republic of Egypt.

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fractional-order differential equations. Furthermore, this paper will present a numerical comparison with some methods, such as legendre operational matrix and pseudo-spectral method. The efficiency and accuracy of the LPS method are demonstrated by two numerical examples.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

Discrete distribution estimation is a fundamental statistical tool, which is widely used to perform data analysis tasks in various applications involving sensitive personal information. Due to privacy concerns, individuals may not always provide their raw information, which leads to unpredictable biases in the final results of estimated distribution. Local Differential Privacy (LDP) is an advanced technique for privacy protection of discrete distribution estimation. Currently, typical LDP mechanisms provide same protection for all items in the domain, which imposes unnecessary perturbation on less sensitive items and thus degrades the utility of final results. Although, several recent works try to alleviate this problem, the utility can be further improved. In this paper, we propose a novel notion called Item-Oriented Personalized LDP (IPLDP), which independently perturbs different items with different privacy budgets to achieve personalized privacy protection. Furthermore, to satisfy IPLDP, we propose the Item-Oriented Personalized Randomized Response (IPRR) based on the observation that the sensitivity of data shows an inverse relationship with the population size of respective individuals. Theoretical analysis and experimental results demonstrate that our method can provide fine-grained privacy protection and improve data utility simultaneously.

This paper is concerned with variational methods for open quantum systems with Markovian dynamics governed by Hudson-Parthasarathy quantum stochastic differential equations. These QSDEs are driven by quantum Wiener processes of the external bosonic fields and are specified by the system Hamiltonian and system-field coupling operators. We consider the system response to perturbations in these operators and introduce a transverse Hamiltonian which encodes the propagation of the perturbations through the unitary system-field evolution. This approach provides an infinitesimal perturbation analysis tool which can be used for the development of optimality conditions in quantum control and filtering problems. Such settings employ, as performance criteria, quadratic (or more complicated) cost functionals of the system and field variables to be minimised over the energy and coupling parameters of system interconnections. We demonstrate an application of the transverse Hamiltonian variational approach to a mean square optimal coherent quantum filtering problem for a measurement-free field-mediated cascade connection of a quantum system with a quantum observer.

Pursuing "intelligent justice" necessitates an impartial, productive, and technologically driven methodology for judicial determinations. This scholarly composition proposes a framework that harnesses Artificial Intelligence (AI) innovations such as Natural Language Processing (NLP), ChatGPT, ontological alignment, and the semantic web, in conjunction with blockchain and privacy techniques, to examine, deduce, and proffer recommendations for the administration of justice. Specifically, through the integration of blockchain technology, the system affords a secure and transparent infrastructure for the management of legal documentation and transactions while preserving data confidentiality. Privacy approaches, including differential privacy and homomorphic encryption techniques, are further employed to safeguard sensitive data and uphold discretion. The advantages of the suggested framework encompass heightened efficiency and expediency, diminished error propensity, a more uniform approach to judicial determinations, and augmented security and privacy. Additionally, by utilizing explainable AI methodologies, the ethical and legal ramifications of deploying intelligent algorithms and blockchain technologies within the legal domain are scrupulously contemplated, ensuring a secure, efficient, and transparent justice system that concurrently protects sensitive information upholds privacy.

The paper's main goal is to introduce a novel type of interpolative convex contraction and build up some fresh findings for it using the interpolative convex contractions' progressive approach. We have established certain conclusions using orbitally S-complete and Suzuki type contractions in F-metric spaces. My research aims to examine the fixed point method's efficacy in solving fractional differential equation with boundary conditions.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for second-order nonlinear differential equations with damping is developed and the limitations of this method are explored. It is shown that the limitations do not exist only for those nonlinear dynamical systems that can be converted into linear ones. The obtained results are applied to selected population dynamics models for which non-standard Lagrangians and their corresponding null Lagrangians and gauge functions are derived, and their roles in the population dynamics are discussed.

The information data accuracy affects the working reliability of production management system directly. Mobile equipment is an important part of integrated manufacturing system, in the course of its works, due to the complex working environment and the dynamic change of its position, it lead to the important problem of information detection distortion. Because the application of fractional differential operator has the dual functions of enhancing signal strength and reducing data error, we puts forward a data processing method of obtaining production information data of various accuracy by changing the parameters of fractional differential operator. Establish a mobile equipment detection data fusion processing model based on fractional order partial differential equations and apply it in the processing experiment of mobile equipment testing information detection data in an integrated manufacturing system, the feasibility and effectiveness of the method are verified. We conclude that the fractional order partial differential equations used in the processing of mobile equipment monitoring information data of an integrated manufacturing system has the function of obtaining production information data of various accuracy, which are of great significance to improve the working reliability in integrated manufacturing system. which is of great significance to improve the working reliability and scientific decision of integrated manufacturing system.

Micro-expression (ME) is one of the key psychological stress reactions. It is a modest, spontaneous facial mechanism. ME has significant applicability in a variety of psychologically-related sectors because to its precision and unpredictability with regard to psychological manifestations. Nevertheless, the current Micro-expression recognition (MER) algorithms have poor accuracy and a limited quantity of ME data, and this study issue has not been thoroughly investigated. Therefore, we present an approach for deep learning based on a Spatio-temporal capsule network (STCP-Net). STCP-Net has four components: a jitter reduction module, a differential feature extraction module, an STCP module, and a fully linked layer. The first two modules are aimed to extract diversifying differential features more precisely and to limit the influence of head jitter. The STCP module is used to extract Spatio-temporal features layer by layer, taking the temporal and geographical connection between features into account. This research runs sufficient trials using the Leave One Subject Out (LOSO) methodology for cross-validation using the CASMEII dataset. The conclusion and analysis demonstrate that the algorithm is innovative and efficient.

Recently, hybrid logic circuits based on magnetic tunnel junctions (MTJs) have been widely investigated to realize zero standby power. However, such hybrid CMOS/MTJ logic circuits suffer from a severe sensing reliability due to the limited tunnel magnetoresistance ratio (TMR≤150%) of the MTJ and the large process variation in the deep sub-micrometer technology node. In this paper, a novel differential sensing amplifier (DSA) is proposed, in which two PMOS transistors are added to connect the discharging branches and evaluation branches. Owing to the positive feedback realized by these two added PMOS transistors, it can achieve a large sensing margin. By using an industrial CMOS 40 nm design kit and a physics-based MTJ compact model, hybrid CMOS/MTJ simulations have been performed to demonstrate its functionality and evaluate its performance. Simulation results show that it can achieve a smaller sensing error rate of 9% in comparison with the previously proposed DSAs with the TMR ratio of 100% and process variation of 10%, while maintaining almost the same sensing delay of 74.5 ps and sensing energy of 1.92 fJ/bit.

Observation of parity-violating effects in chiral molecules is a long-standing challenge of the molecular spectroscopy community. In the microwave regime, the difference in transition frequencies between enantiomers is predicted to be below the mHz level, which is considerably beyond current experimental capabilities. The most promising future efforts combine vibrational spectroscopy, buffer gas cooling, and carefully chosen molecular candidates with large predicted parity-violating shifts. Here, we demonstrate for the first time high-precision differential microwave spectroscopy, achieving sub-Hz precision by coupling a cryogenic buffer gas cell with a tunable microwave Fabry-Perot cavity. We report statistically limited sub-Hz precision of (0.08±0.72) Hz, observed between enantiopure samples of (R)-1,2-propanediol and (S)-1,2-propanediol at frequencies near 15 GHz. We confirm highly repeatable spectroscopic measurements compared to traditional pulsed-jet methods, opening up new capabilities in probing subtle molecular structural effects at the 10−10 level and providing a platform for exploring sources of systematic error in parity-violation searches. We discuss dominant systematic effects at this level and propose possible extensions of the technique for higher precision.

The methods for constructing solutions to integro-differential equations of the Volterra type are considered. The equations are related to fractional conformable derivatives. Explicit solutions of homogeneous and inhomogeneous equations are constructed and a Cauchy-type problem is studied. It should be noted that the considered method is based on the construction of normalized systems of functions with respect to a differential operator of fractional order.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

YH-DIE must have continuity . Given the basic algebraic clusters of homogeneous configurations,we can get the basic three equations: \begin{array}{l} {\mathop{\int}\nolimits_{0}\nolimits^{{x}_{i}}{\frac{{G}\left({{x}_{i}\mathrm{,}s}\right)}{{\left({{x}_{i}\mathrm{{-}}{s}}\right)}^{\mathit{\alpha}}}\mathrm{\varphi}\left({s}\right){ds}}\mathrm{{=}}{f}\left({{x}_{i}}\right)}\ ;\ {\frac{\mathrm{\partial}}{\mathrm{\partial}{x}_{i}}\left({\frac{{\mathrm{\partial}}_{{x}_{i}}G}{\sqrt{{1}\mathrm{{+}}{\left|{\mathrm{\nabla}{G}}\right|}^{2}}}}\right)\mathrm{{=}}{0}}\ ;\ {{i}\mathrm{{=}}\mathop{\sum}\limits_{{x}_{i}\mathrm{{=}}{1}}\limits^{\mathrm{\infty}}{\arccos\hspace{0.33em}\mathrm{\varphi}\left({{x}_{i}}\right)}\mathrm{{=}}{f}\left({\fbox{${Yuh}$}}\right)} \end{array} YH-DIE has become a fusion point and access point in the fields of algebraic geometry and partial differential equations, and its mapping on multidimensional algebraic clusters or manifolds is very special. The minimal surface equation is a special case.

In this paper, we introduce some basic idea of Variational iteration method for short (VIM) to solve the Volterra’s integro-differential equations. The VIM is used to solve effectively, easily, and accurately a large class of non-linear problems with approximations which converge rapidly to accurate solutions. For linear problems, it’s exact solution can be obtained by only one iteration step due to the fact that the Lagrange multiplier can be exactly identified. It is to be noted that the Lagrange multiplier reduces the iteration on integral operator and also minimizes the computational time. The method requires no transformation or linearization of any forms. Two numerical examples are presented to show the effectiveness and efficiency of the method. Also, we compare the result with the result from Homotopy perturbation method (HPM). Finally, we investigate the absolute difference between variational iteration method and homotopy perturbation method and draw the graph of difference function by using Mathematica.

In this paper, we study the entire or meromorphic solutions for differential-difference equations in f(z) , its shifts, its derivatives and derivatives of its shifts. and study some Hayman's results for differential-difference polynomials.

This paper presents an extension for principles of Differential Geometry on Surfaces (re-hashed through the budding field of CMS, the Calculus of Moving Surfaces). It analyzes mostly 2D Hypersurfaces with Riemannian Geometry and proposes the construction of a 3D Static Frame combining the Surface Basis Vectors with the Orthogonal Normal Field as a 3D Orthogonal Vector Frame. The paper introduces conventions for manipulating Tensors defined using this 3D Orthogonal Vector Frame as well as Curvature Connections associated with this Vector Frame. It then finally introduces Symbols and Tensors to describe Inner Products and Variance within the 3D Vector Frame and then extends all the above concepts to a surface which is Dynamic utilizing principles from CMS. This formulation has potential to extend identities and concepts from CMS and from Differential Geometry in a compact Tensorial Framework, which agrees with the new Framework proposed by CMS.

We have recently solved the tumbling-snake model for concentrated polymer solutions and entangled melts in the presence of both steady-state and transient shear and uniaxial elongational flows, supplemented by a variable link tension coefficient. Here, we provide the transient and stationary solutions of the tumbling-snake model under biaxial elongation both analytically, for small and large elongation rates, and via Brownian dynamics simulations, for the case of planar elongational flow over a wide range of rates, times, and the model parameters. We show that both the steady-state and transient first planar viscosity predictions are similar to their uniaxial counterparts, in accord with recent experimental data. The second planar viscosity seems to behave in all aspects similarly to the shear viscosity, if shear rate is replaced by elongation rate.

In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on the left hand side. We prove a theorem on the solution of the linear system of equations, which collapses to the well-known Mittag-Leffler solution in the case the indices are the same, and also generalises the solution of the so-called linear sequential class of time fractional problems. We also investigate the asymptotic stability properties of this class of problems using Laplace transforms and show how Laplace transforms can be used to write solutions as linear combinations of generalisedMittag-Leffler functions in some cases. Finally we illustrate our results with some numerical simulations.

A cuprous oxide (Cu₂O) thin layer served as the base for a non-enzymatic glucose sensor in an alkaline medium, 0.1 NaOH solution, with a linear range of 50-200 mg/dL using differential pulse voltammetry (DPV) measurement. An X-ray photoelectron spectroscopy (XPS) study confirmed the formation of the cuprous oxide layer on the thin gold film sensor prototype. Quantitative detection of glucose in both phosphate-buffered saline (PBS) and undiluted human serum were carried out. Neither ascorbic acid nor uric acid even at a relatively high concentration level of 100mg/dL in serum interfered with the glucose detection, demonstrating the excellent selectivity of this non-enzymatic cuprous oxide thin layer based glucose sensor. Chronoamperometry (CA) and single potential amperometric voltammetry were used to verify the measurements obtained by differential pulse voltammetry (DPV), and the positive results validated that the detection of glucose in a 0.1 M NaOH alkaline medium by DPV measurement was effective. Nickel, platinum and copper are commonly used metals for non-enzymatic glucose detection. The performance of these metal-based sensors for glucose detection using DPV were also evaluated. Cuprous oxide (Cu₂O) thin layer based sensor showed the best sensitivity for glucose detection among the sensors evaluated.

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion of nano-beam. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of value and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency ratio and imperfection sensitivity of a curved SWCNT for various boundary conditions are investigated. The results show that the geometric imperfection plays a significant role in the nonlinear vibration characteristics of curved SWCNTs.

In engineering practice, various types of information data are affected by many factors during the collection process. For example, information data measurement errors are caused by equipment performance and the working environment. During the transmission of detection information, the signal distortion caused by energy loss and signal interference causes unpredictable detection errors in the collected information data. Through the study of fractional calculus theory, it was found that it is suitable for studying nonlinear, non-causal, and non-stationary signals, and has the dual functions of improving detection information and enhancing signal strength. Therefore, under the influence of many factors, we applied the fractional difference algorithm to the field of information data processing. Multi-sensor detection data fusion algorithm based on the fractional partial differential equation was adopted to establish its online detection data. A multi-sensor detection data fusion algorithm based on a fractional partial differential equation is established, which effectively fuses the information data detection errors caused by various influencing factors and greatly improves the detection accuracy of information data. The effectiveness of this method is proved through its application in an experiment.

Pregnancy is a dynamic state with multiple metabolic changes occurring including insulin resistance. Gestational diabetes mellitus (GDM), a form of diabetes that appears during pregnancy, develops if metabolic aberrations occur, in particular, in normal pregnancy-induced insulin resistance. Multi-omics is a powerful approach for uncovering the mechanisms driving metabolic change in different physiologic and pathologic states. A recent study demonstrated that the gestational gut microbiome mediates pregnancy metabolic adaptations through effects on gut indoleamine-2,3 dioxygenase 1 activity and the production of kynurenine. Using the dataset generated from this highly controlled study, we performed a comprehensive analysis of the pregnancy-specific physiological and metabolic profiles, 16S rRNA microbiome, and plasma untargeted LC-MS metabolome data. To facilitate the utilization of these analysis results by other researchers, we developed MOMMI-MP, a database that provides an easy-to-use platform to browse and search differential abundant microbial taxa and metabolites, and to examine metabolic pathways. The datasets consist of data collected from 3 genetically diverse strains of mice (C57BL/6J, CD1, and NIH-Swiss) over 6 time points during the gestational (days 0, 10, 15, and 19 during gestation) and postpartum (days 3 and 20 after delivery) states, totaling 180 samples for each strain. The computational results are presented in various tables and plots, and organized in MOMMI-MP to empower exploratory analyses by other researchers. In conclusion, MOMMI-MP is a resource to facilitate the investigation of novel mechanisms governing metabolic changes during pregnancy.

To assess the degree to which it has met its commitments under the Paris Agreement, Morocco is called upon to carry out carbon assessments and transparent evaluations. Within the forestry sector, little is known about the role of Morocco’s forests in contributing to carbon uptake. With this aim, we applied for the first time in literature the 3-PG model to Cedrus atlantica ((Endl.) Manetti ex Carrière, 1855), which represents about 131.800 ha of Morocco’s forest area (i.e. Azrou forest). Through the Differential Evolution - Markov Chains (DE-MC) we tested and assessed the sensitivity and calibrated the 3-PG model. This process-based model provided significant results regarding the carbon sequestration capacity. The results showed the following: i- Parameters related to stand properties, canopy structure, and processes, as well as biomass partitioning, are the most important or sensitive for the performance of the model; ii- The DE-MC method optimized the values of the 3-PG parameters which was confirmed by the means of Gelman-Rubin convergence test; iii- According to the predictions of the calibrated 3-PG, the Net Primary Production in the pure Azrou forest varies between 0.32 and 7.88 tC.ha−1.yr−1, it is equal in average to 4.9 tC.ha−1.yr−1, which given the total area corresponds to 7078 tC.yr−1.

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

A plant’s early response to pathogen stress is a vital indicator of its disease resistance. In order to study the response mechanism of resistant and susceptible flax cultivars to Fusarium oxysporum f. sp. lini (Foln), we applied RNA-sequencing to analyze transcriptomes of flax with Foln 0.5, 2 and 8 hours post inoculation (hpi). We found a significant difference in the number of differential expression genes (DEGs) between resistant and susceptible flax clutivars. The number of DEGs in the Fusarium-resistant cultivar increased dramatically at 2 hpi, and a large number of DEGs participated in the Fusarium-susceptible cultivar response to Foln infection 0.5 hpi. GO enrichment analysis determined that the up-regulated DEGs of both flax cultivars were enriched such as oxidoreductase activity and oxidation-reduction process. At the same time, the genes involved in diterpenoid synthesis were up-regulated in resistant cultivar, while those involved in extracellular region, cell wall and organophosphate ester transport were down-regulated in susceptible cultivar. KEGG enrichment analysis showed the genes encoded WRKY 22 and WRKY33 which involved in MAPK signaling pathway were up-regulated expressed in S-29 and down-regulated expressed in R-7, negatively regulated the disease resistance of flax; The genes encoded Hsp 90 family which in involved in plant pathogen interaction pathway were up-regulated in R-7 and down-regulated in S-29, which positively regulated the disease resistance of flax; The genes encoded MYC2 transcription factor and TIFY proteins which involved in plant hormone signaling pathway were up-regulated in R-7, and regulated the jasmonic acid metabolism of flax and the signal transduction of plant hormones. Meanwhile seven regulatory genes with the most correlation were screened out, Among Lus10025000.g and Lus10026447.g regulated other genes expressed both in plant hormone signal transduction pathway and MAPK signal pathway. In conclusion, these findings will facilitate further studies on the function of these candidate genes in flax of response to Fusarium stress, and the breeding of disease-resistant flax cultivar.

In this paper, a multi-operator differential evolution algorithm (MODE) is proposed to solve the Optimal Power Flow (OPF) problem and is called MODE-OPF. The MODE-OPF utilizes the strengths of more than one differential evolution (DE) operator in a single algorithmic framework. Additionally, an adaptive method (AM) is proposed to update the number of solutions evolved by each DE operator based on both the diversity of population and quality of solutions. This adaptive method has the ability to maintain diversity at the early stages of the optimization process and boost convergence at the later ones. The performance of the proposed MODE-OPF is tested by solving OPF problems for both small and large IEEE bus systems (i.e., IEEE-30 and IEEE-118) while considering the intermittent solar and wind power generation. To prove the suitability of this proposed algorithm, its performance has been compared against several state-of-the-art optimization algorithms, where MODE-OPF outperforms other algorithms in all experimental results and thereby improving a network's performance with lower cost. MODE-OPF decreases the total generation cost up to 24.08%, the real power loss up to 6.80% and the total generation cost with emission up to 8.56%.

In this article, we are interested in a new generic class of nonlocal fractional impulsive differential inclusions with linear sectorial operator and Lipschitz multivalued function in the setting of finite dimensional Banach spaces. By modifying the definition of PC-mild solutions initiated by Shu, we succeeded to determine new conditions that sufficiently guarantee the existence of the solutions. The results are obtained by combining techniques of fractional calculus and fixed point theorem for contraction maps. We also characterize the topological structure of the set of solutions. Finally, we provide a demonstration to address the applicability of the theoretical results.

A linear Cauchy problem with polynomial coefficients wich combines q-difference operators for q>1 and differential operators of irregular type is examined. A finite set of sectorial holomorphic solutions w.r.t the complex time is constructed by means of classical Laplace transforms. These functions share a common asymptotic expansion in the time variable which turns out to carry a double layers structure which couples q-Gevrey and Gevrey bounds. In the last part of the work, the problem of confluence of these solutions as q tends to 1 is investigated.