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By taking the ultra-spinning limit as a simple solution-generating trick, a novel class of ultra-spinning charged black hole solutions has been constructed from Chow's rotating charged black hole with two equal-charge parameters in six-dimensional $\mathcal{N} = 4$ gauged supergravity theory. We investigate their thermodynamical properties and then demonstrate that all thermodynamical quantities completely obey both the differential first law and the Bekenstein-Smarr mass formula. For the six-dimensional ultra-spinning Chow's black hole with only one rotation parameter, we show that it does not always obey the reverse isoperimetric inequality, thus it can be either sub-entropic or super-entropic, depending upon the ranges of the mass parameter and especially the charge parameter. This property is obviously different from that of the six-dimensional singly-rotating Kerr-AdS super-entropic black hole, which always strictly violates the RII. For the six-dimensional doubly-rotating Chow's black hole but ultra-spinning only along one spatial axis, we point out that it may also obey or violate the RII, and can be either super-entropic or sub-entropic in general., 22 pages, 8 figures, 3 tables, match the published version of JHEP

MotivationAnalyzing tandem mass spectrometry data to recognize peptides in a sample is the fundamental task in computational proteomics. Traditional peptide identification algorithms perform well when identifying unmodified peptides. However, when peptides have post-translational modifications (PTMs), these methods cannot provide satisfactory results. Recently, Chick et al., 2015 and Yu et al., 2016 proposed the spectrum-based and tag-based open search methods, respectively, to identify peptides with PTMs. While the performance of these two methods is promising, the identification results vary greatly with respect to the quality of tandem mass spectra and the number of PTMs in peptides. This motivates us to systematically study the relationship between the performance of open search methods and quality parameters of tandem mass spectrum data, as well as the number of PTMs in peptides.ResultsThrough large-scale simulations, we obtain the performance trend when simulated tandem mass spectra are of different quality. We propose an analytical model to describe the relationship between the probability of obtaining correct identifications and the spectrum quality as well as the number of PTMs. Based on the analytical model, we can quantitatively describe the necessary condition to effectively apply open search methods.AvailabilitySource codes of the simulation are available at http://bioinformatics.ust.hk/PST.html.Contactboningli@ust.hk or eeyu@ust.hkSupplementary informationSupplementary data are available at Bioinformatics online.

The functional connectivity provides new insights into the mechanisms of the human brain at network-level, which has been proved to be an effective biomarker for brain disease classification. Recently, machine learning methods have played an important role in functional connectivity classification, among which convolutional neural network (CNN) based methods become a new hot topic since they can extract topological features in the brain network. However, the conventional CNN-based methods haven't taken sparse connectivity patterns (SCPs) of the human brain into consideration, which may lead to redundancy of the topological features, and limit their performance and generalization. To solve it, we propose a novel CNN-based model with graphical Lasso (CNNGLasso) to extract sparse topological features for brain disease classification. Firstly, we develop a novel graphical Lasso model for revealing the SCPs at group-level. Then, the SCPs are used to guide the topological feature extraction. Finally, the obtained sparse topological features are used to classify the patients from normal controls. The experiment results on the ABIDE dataset demonstrate that the CNNGLasso outperforms the others on various performances. Besides, the abnormal brain regions derived from the trained model are consistent with the previous investigations, which further proves the application prospect of the CNNGLasso.

The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the $$ \mathcal{N} $$ N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.

Accurate estimation of remaining useful life (RUL) of industrial equipment can enable advanced maintenance schedules, increase equipment availability and reduce operational costs. However, existing deep learning methods for RUL prediction are not completely successful due to the following two reasons. First, relying on a single objective function to estimate the RUL will limit the learned representations and thus affect the prediction accuracy. Second, while longer sequences are more informative for modelling the sensor dynamics of equipment, existing methods are less effective to deal with very long sequences, as they mainly focus on the latest information. To address these two problems, we develop a novel attention-based sequence to sequence with auxiliary task (ATS2S) model. In particular, our model jointly optimizes both reconstruction loss to empower our model with predictive capabilities (by predicting next input sequence given current input sequence) and RUL prediction loss to minimize the difference between the predicted RUL and actual RUL. Furthermore, to better handle longer sequences, we employ the attention mechanism to focus on all the important input information during the training process. Finally, we propose a new dual-latent feature representation to integrate the encoder features and decoder hidden states, to capture rich semantic information in data. We conduct extensive experiments on four real datasets to evaluate the efficacy of the proposed method. Experimental results show that our proposed method can achieve superior performance over 13 state-of-the-art methods consistently.

Experiencing homelessness is traumatizing and can exacerbate mental illnesses and substance use disorders. When persons experiencing homelessness are a danger to themselves or others, petitioning for involuntary placement is clinically, ethically, and legally indicated. The process of involuntary commitment is often traumatic and can fracture already fragile relationships that persons experiencing homeless have; involuntary commitment should be used only when necessary. It is society's obligation to prevent crises but, when needed, to support persons in crisis by responding with care to their health needs.

This paper studies the heavy-traffic limit of the moments of the stationary distribution in GI/G/1-type Markov chains. For these Markov chains, several researchers have derived heavy-traffic-limit formulas for the stationary distribution itself. However, for its moments, no such formulas have been reported in the literature. This paper presents a heavy-traffic-limit formula for the moments of the stationary distribution and a sufficient condition for the formula to hold, by using a characteristic function approach.

In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term appears. Such a term is explicitly given in terms of the solution of Poisson equation in Hilbert space. Moreover, we also obtain the optimal rate of convergence, and the convergence rate is shown not to depend on the regularity of the coefficients of the original system with respect to the fast variable, which coincides with the intuition since the fast component has been totally homogenized out in the limit equation., arXiv admin note: text overlap with arXiv:2010.14897

We review the optimal booking limit in the two-class static revenue management model with customers’ buy-up behavior. This is when a deterministic fraction of the low-fare customer class that cannot book early are willing to book the higher fare later. This simple model with dependent demands is difficult to analyze. Some well-known publications, such as Talluri and van Ryzin ( 2004 ) and Phillips ( 2005 ), treat this model incorrectly. In this note, we correct an erroneous formula for the modified fare ratio with the proper probabilistic interpretation. The correction was established previously by Brumelle et al. ( 1990 ). Numerical examples reveal that the corrected modified fare ratio provides a lower optimal booking limit, resulting in a higher expected revenue than those obtained by using the incorrect modified fare ratio.

We investigate strong stability preserving (SSP) implicit-explicit (IMEX) methods for partitioned systems of differential equations with stiff and nonstiff subsystems. Conditions for order p and stage order $$q=p$$ q = p are derived, and characterization of SSP IMEX methods is provided following the recent work by Spijker. Stability properties of these methods with respect to the decoupled linear system with a complex parameter, and a coupled linear system with real parameters are also investigated. Examples of methods up to the order $$p=4$$ p = 4 and stage order $$q=p$$ q = p are provided. Numerical examples on six partitioned test systems confirm that the derived methods achieve the expected order of convergence for large range of stepsizes of integration, and they are also suitable for preserving the accuracy in the stiff limit or preserving the positivity of the numerical solution for large stepsizes.

The logic $${\mathbb{L}}_\theta ^1$$ was introduced in [She12]; it is the maximal logic below $${{\mathbb{L}}_{\theta, \theta}}$$ in which a well ordering is not definable. We investigate it for θ a compact cardinal. We prove that it satisfies several parallels of classical theorems on first order logic, strengthening the thesis that it is a natural logic. In particular, two models are $${\mathbb{L}}_\theta ^1$$ -equivalent iff for some ω-sequence of θ-complete ultrafilters, the iterated ultrapowers by it of those two models are isomorphic. Also for strong limit λ>θ of cofinality $${\aleph _0}$$ , every complete $${\mathbb{L}}_\theta ^1$$ -theory has a so-called special model of cardinality λ, a parallel of saturated. For first order theory T and singular strong limit cardinal λ, T has a so-called special model of cardinality λ. Using “special” in our context is justified by: it is unique (fixing T and λ), all reducts of a special model are special too, so we have another proof of interpolation in this case.

The results of experimental studies have shown a strong effect of diffusion hydrogen on the static and cyclic parameters of crack resistance of reinforcing steel. It was found that with increasing flooding, especially when the hydrogen content exceeds 5 cm3/100g, both static strength and long-term strength (fatigue) decrease sharply. Moreover, these areas of hydrogen solution in reinforcing steel are characterized by a viscous nature of fracture, while for heavily flooded reinforcement (from 5 to 12 cm3/100g) is characterized by brittle fracture by the mechanism of microcracking in the hardened (martensite or troostite structure). The analysis of the obtained experimental results allowed to determine the optimal hydrogen content in the reinforcing steel (3…5 cm3/100g), the excess of which can cause a decrease in the crack resistance of the reinforcement during long-term operation, especially in corrosive environments. The mechanism of hydrogen influence on crack resistance of metal at static and alternating loading which consists in diffusion and dislocation movement of hydrogen in structure of a reinforcing core that as a result that causes strong flooding of steel and its embrittlement is offered. It is established that carbon and low-alloy sieves, which are characterized by ferritic-pearlitic and sorbitol structure provide high resistance, especially to long-term fatigue, and the transition to steels with a structure of martensite or tempered (transient structure of bainite) structure of bainite sharply reduces reinforcing steel, which makes it impossible to use in the manufacture of reinforcement involved in reinforced concrete structures designed for long-term operation (more than 50…60 years). Thus, the obtained diagram can be recommended to designers of reinforced concrete structures for hydraulic purposes, as it greatly facilitates the reasonable choice of reinforcement in the development of reinforced concrete structures for responsible and long-term use.

To identify how FOUL is investigated in patients with PD.The Preferred Reporting Items for Systematic Reviews guideline was used, and the search was carried out in four databases, with no limit on ...

Critical urban thinkers often imagine urbanisation and the Anthropocene as inevitably being companion processes. But is planetary urbanisation the necessary telos and spatial limit of life in the Anthropocene? Is urban resilience the final form of urban responses to climate change? Will (or should) the urban (as either spatial form or process) survive the upending impacts of climate change or adaptation? Or, if the Anthropocene is a time of deep environmental and epistemological upheaval without historical precedent, might even more recently created spatial concepts of the planetary urban condition themselves soon be out of date? This article raises these questions for urban scholars via critical engagement with a proposal to retire Miami – considered climate change ‘ground zero’ in the US and doomed by rising seas – and repurpose it as fill for ‘The Islands of South Florida’: a self-sufficient territory of artificial high-rises delinked from global infrastructural networks. This vision of an ‘urbicidal Anthropocene’, the article argues, suggests that the injunction subtending planetary urbanisation work – to relentlessly question inherited spatial frameworks – has not been taken far enough. Still needed is Anthropocene critical urban theory, to consider urban forms and processes emerging via climate change and adaptation, but also how such mutations may point beyond the theoretical and spatial bounds of the contemporary urban condition itself.

Totally symmetric self-complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well-known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in one-twelfth of a hexagon with free boundary to express them as perfect matchings of a family of non-bipartite planar graphs. Our main result is that the edges of the TSSCPPs form a Pfaffian point process, for which we give explicit formulas for the inverse Kasteleyn matrix. Preliminary analysis of these correlations are then used to give a precise conjecture for the limit shape of TSSCPPs in the scaling limit., 38 pages, 14 figures, minor corrections, final version

In this paper we determine two asymptotic results for Jack measures on partitions, a model defined by two specializations of Jack polynomials proposed by Borodin-Olshanski in [European J. Combin. 26.6 (2005): 795-834]. Assuming these two specializations are the same, we derive limit shapes and Gaussian fluctuations for the anisotropic profiles of these random partitions in three asymptotic regimes associated to diverging, fixed, and vanishing values of the Jack parameter. To do so, we introduce a generalization of Motzkin paths we call "ribbon paths", show for general Jack measures that certain joint cumulants are weighted sums of connected ribbon paths on $n$ sites with $n-1+g$ pairings, and derive our two results from the contributions of $(n,g)=(1,0)$ and $(2,0)$, respectively. Our analysis makes use of Nazarov-Sklyanin's spectral theory for Jack polynomials. As a consequence, we give new proofs of several results for Schur measures, Plancherel measures, and Jack-Plancherel measures. In addition, we relate our weighted sums of ribbon paths to the weighted sums of ribbon graphs of maps on non-oriented real surfaces recently introduced by Chapuy-Dol\k{e}ga., Comment: Several results in this paper first appeared in the author's unpublished monograph arXiv:1508.03063. Version 2: revised and accepted for publication in International Mathematics Research Notices (IMRN)

Tests that fail inconsistently, without changes to the code under test, are described as flaky . Flaky tests do not give a clear indication of the presence of software bugs and thus limit the reliability of the test suites that contain them. A recent survey of software developers found that 59% claimed to deal with flaky tests on a monthly, weekly, or daily basis. As well as being detrimental to developers, flaky tests have also been shown to limit the applicability of useful techniques in software testing research. In general, one can think of flaky tests as being a threat to the validity of any methodology that assumes the outcome of a test only depends on the source code it covers. In this article, we systematically survey the body of literature relevant to flaky test research, amounting to 76 papers. We split our analysis into four parts: addressing the causes of flaky tests, their costs and consequences, detection strategies, and approaches for their mitigation and repair. Our findings and their implications have consequences for how the software-testing community deals with test flakiness, pertinent to practitioners and of interest to those wanting to familiarize themselves with the research area.

We developed in this work the computation of the volume of the sphere via the method of exhaustion by inscribed truncated right cones. We show that this computation can be used in calculus courses in several ways; mainly, to motivate and clarify the usage of the squeeze theorem in the computations of sum limits. As a result, we generalized a sum limit using Bernoulli numbers, producing a magnificent example of applied mathematics, and highlighting the importance of exploring when studying mathematics.

Limit theorems for sub-linear expectations are challenging field which have raised a large number of issues of interest recently. The aim of this article is to establish the strong limit theorems o...

Based on the first-order second-moment method, a comparative study on seismic fragility analysis with consideration of modeling uncertainty is carried out for a 12-story reinforced concrete frame structure under excitation with far-field and pulse-like near-field ground motions by using the multiple stripes analysis method. The sensitivity of the median fragility capacity of the building to fourteen parameters in the cases of three limit states (i.e., immediate occupancy, life safety, and collapse prevention) is analysed, and the effect of the selection of ground motion intensity measures on the determination of modeling uncertainty is investigated. Finally, the annual probabilities of exceeding each limit state with different confidence levels are calculated, and two methods, the mean estimates approach and the confidence interval method, are used to incorporate uncertainties. The results show that the characteristics of ground motions affect the sensitivity of the median capacity to the disturbance of structural parameters. The modeling uncertainty estimated in the near-field records is meaningfully less than that in the far-field records. Judging from this limited case study, the modeling uncertainty estimated may be underestimated by using an inefficient IM. The influence of the modeling uncertainty in the fragility analysis for each limit state cannot be ignored when using the confidence interval method.

At present, the deep learning super-resolution (SR) method has achieved excellent results, but it also faces problems such as large models, high computational cost, a large amounts of training data, and poor interpretability. However, traditional machine learning-based methods still have room for improvement in feature extraction and model structure. This paper constructs a gradient embedding cascade forest structure on the basis of random forest and proposes a limit gradient embedding cascaded forest SR (LGECFSR) model. In feature construction, we not only adopt the first-order gradient, the second-order gradient, and other features of the image but also fuse the information of the original LR image. In addition, image blocks of different sizes are used for training, which increases the model’s generalization ability. Compared with the state-of-the-art machine learning-based methods, our method achieves the best performance and the second-best computational speed. In addition, compared with some deep learning-based methods, our model has a similar reconstruction effect and the best computational speed. In detail, for some reconstruction tasks, the Multi-Adds of LGECFSR is one-tenth to one-4000th of that of some current models. However, the SR performance of LGECFSR is the same or slightly better than that of some current classical algorithms.

We provide a large deviation principle on the stochastic differential equations with reflecting Wentzel boundary condition if δ ε {\frac{\delta}{\varepsilon}} tends to 0 when the two parameters δ (homogenization parameter) and ε (the large deviations parameter) tend to zero. Here, we suppose that the homogenization parameter converges sufficiently quickly more than the large deviations parameter. Furthermore, we will make explicit the associated rate function.

Tailor rolled blank (TRB) with graded thickness has shown great potential in the automobile field. Using traditional forming limit diagrams (FLDs) to evaluate TRB formability is challenging due to thickness variations. In this paper, a 3D forming limit surface (FLS) considering the influence of thickness was obtained. A numerical model was developed to predict final strains. Moreover, a forming margin was denoted and calculated to generate the forming limit margin field graph for quantitative evaluation of the TRB formability. Results showed that as the punch travel increased, the forming margin value decreased. As the travel changed from 35.2 mm to 37.4 mm, the corresponding forming margin value changed from 0.002 to −0.024. The formability declined, and the specimen eventually cracked on the thinner side. Besides, the deformation and strain paths predicted by simulation agreed well with those measured from formed part, which indicated that the final strains used in formability evaluation were reliable. The method was suitable for quantitative evaluation of the formability and predicting the cracking position in TRB forming.

The fundamental mission of a distribution network is to satisfy the customer demand by providing sufficient delivery capacity. However, the capacity of a distribution network is practically stochastic because of unexpected events, and moreover, the commodities may rot or be spoilt during delivery owing to inclement weather, traffic accidents, collisions, and so on, such that the intact commodity flow may not meet market demand. This paper focuses on the reliability of a multi-state distribution network (MSDN) with cost and spoilage characteristics, defined as the probability that the MSDN is able to distribute a sufficient quantity of goods to meet the market demand under delivery spoilage and budget limit considerations. A specific spoilage rate associated with each route is adopted to characterize the perishability of commodity flows, and the critical routes whose spoilage rate change has the biggest impact on network reliability are identified with the use of sensitivity analysis method. Apart from delivery cost, the cost involved with the disposal of spoilt goods is also incorporated into the reliability indicator. A minimal paths based algorithm is presented to calculate network reliability, together with an example to illustrate the procedure. A real fruit distribution network is accordingly discussed to demonstrate the utility of the algorithm and the managerial implication of network reliability.

An important component of Apery’s proof that ζ(3) is irrational involves representing ζ(3) as the limit of the quotient of two rational solutions to a three-term recurrence. We present various appr...

An analytical approach is constructed to examine the limit stresses of multilayered fiber reinforced disk. Three different layer configurations are considered, which are decreasing, constant and in...

We shall prove the validity of the Prandtl boundary layer expansion for the two-dimensional Navier-Stokes flows around the Rayleigh boundary layer, which is the first result verifying the stability of the formation of the boundary layer in the inviscid limit with respect to the perturbations in the Gevrey $$\frac{3}{2}$$ class.

The subject of research in the article is sigularly perturbed controllable systems of differential equations containing terms with a small parameters on the right-hand side, which are not completely known, but only satisfy some constraints. The aim of the work is to expand the study of the behavior of solutions of singularly perturbed systems of differential equations to the case when the system is influenced not only by dynamic (small factor at the derivative) but also parametric (small factor at the right side of equations) uncertainties and to determine conditions under which such systems will be asymptotically resistant to any perturbations, estimate the upper limit of the small parameter, so that for all values of this parameter less than the obtained estimate, the undisturbed solution of the system was asymptotically stable. The following problems are solved in the article: singularly perturbed systems of differential equations with regular perturbations in the form of terms with a small parameter in the right-hand sides, which are not fully known, are investigated; an estimate is made of the areas of asymptotic stability of the unperturbed solution of such systems, that is, the class of systems that can be investigated for stability is expanded, the formulas obtained that allow one to analyze the asymptotic stability of solutions to systems even under conditions of incomplete information about the perturbations acting on them. The following methods are used: mathematical modeling of complex control systems; vector Lyapunov functions investigation of asymptotic stability of solutions of systems of differential equations. The following results were obtained: an estimate was made for the upper bound of a small parameter for sigularly perturbed systems of differential equations with fully known parametric (fully known) and dynamic uncertainties, such that for all values of this parameter less than the obtained estimate, such an unperturbed solution is asymptotically stable; a theorem is proved in which sufficient conditions for the uniform asymptotic stability of such a system are formulated. Conclusions: the method of vector Lyapunov functions extends to the class of singularly perturbed systems of differential equations with a small factor in the right-hand sides, which are not completely known, but only satisfy certain constraints., Предметом исследования в статье является сигулярно возмущенные управляемые системы дифференциальных уравнений, содержащих слагаемые с малым множителем в правой части, которые не являются полностью известными, а лишь удовлетворяют некоторым ограничениям. Цель работы – расширить исследование поведения решений сигулярно возмущенных систем дифференциальных уравнений на случай, когда на систему влияют не только динамические (малый множитель при производной), но и параметрические (малый множитель в правой части уравнений) неопределенности и определить условия, при которых решения таких систем будут асимптотически устойчивыми к любым возмущениям , оценить верхнюю границу малого параметра, таким образом что для всех значений этого параметра, меньших чем полученная оценка, невозмущенное решение системы являлось асимптотически устойчивым. В статье решаются следующие задачи: исследуются сингулярно возмущенные системы дифференциальных уравнений, имеющих регулярные возмущения в виде слагаемых с малым множителем в правых частях, которые не являются полностью известными; делается оценка областей асимптотической устойчивости невозмущенного решения таких систем, то есть расширяется класс систем, которые можно исследовать на устойчивость, получены формулы, позволяющие анализировать асимптотической устойчивости решений систем даже в условиях неполной информаций о возмущения, действующие на них. Используются такие методы: математическое моделирование сложных систем управления; векторные функции Ляпунова исследования асимптотической устойчивости решений систем дифференциальных уравнений. Получены следующие результаты: сделана оценка верхней границы малого параметра для сигулярно возмущенных систем дифференциальных уравнений с параметрическими (не полностью известными) и динамическими неопределенностями, такая что для всех значений этого параметра, меньших чем полученная оценка, невозмущенное решение такой является асимптотически устойчивым; доказана теорема, в которой сформулированы достаточные условия равномерной асимптотической устойчивости такой системы. Выводы: метод векторных функций Ляпунова может быть расширен на класс сингулярно возмущенных систем дифференциальных уравнений с малым множителем в правых частях, которые не являются полностью известными, а лишь удовлетворяют некоторым ограничениям., Предметом дослідження в статті є сигулярно збурені керовані системи диференціальних рівнянь, що містять доданки з малим множником у правій частині, які не є повністю відомими, а лише задовольняють деяким обмеженням. Мета роботи — поширити дослідження поведінки розв’язків сигулярно збурених систем диференціальних рівнянь на випадок, коли на систему впливають не тільки динамічні (малий множник при похідній), а ще і параметричні (малий множник у правій частині рівнянь) невизначеності та визначити умови, за яких розв’язки таких систем будуть асимптотично стійкими до будь-яких збурень, оцінити верхню границю малого параметру, таким чином що для всіх значень цього параметру, менших ніж отримана оцінка, незбурений розв’язок системи є асимптотично стійким. В статті вирішуються наступні завдання: досліджуються сингулярно збурені системи диференціальних рівнянь, що мають регулярні збурення у вигляді доданків з малим множником у правих частинах, які не є повністю відомими; робиться оцінка областей асимптотичної стійкості незбуреного розв’язку таких систем, тобто розширюється клас систем, які можна досліджувати на стійкість, отримуються формули, що дозволяють аналізувати асимптотичну стійкість розв’язків систем навіть за умов неповної інформацій про збурення, що діють на них. Використовуються такі методи: математичне моделювання складних систем керування; векторні функції Ляпунова дослідження асимптотичної стійкості розв’язків систем диференціальних рівнянь. Отримано наступні результати: зроблена оцінка верхньої границі малого параметра для сигулярно збурених систем диференціальних рівнянь параметричними (неповністю відомими) і динамічними невизначеностями , така що для всіх значень цього параметру, менших ніж отримана оцінка, незбурений розв’язок такої є асимптотично стійким; доведена теорема, в якій сформульовані достатні умови рівномірної асимптотичної стійкості такої системи. Висновки: метод векторних функцій Ляпунова може бути поширеним на клас сингулярно збурених систем диференціальних рівнянь з малим множником у правих частинах, які не є повністю відомими, а лише задовольняють деяким обмеженням.

Consider Jacobi random matrix ensembles with the distributions $$c_{k_1,k_2,k_3}\prod_{1\leq i< j \leq N}\left(x_j-x_i\right)^{k_3}\prod_{i=1}^N \left(1-x_i\right)^{\frac{k_1+k_2}{2}-\frac{1}{2}}\left(1+x_i\right)^{\frac{k_2}{2}-\frac{1}{2}} dx$$ of the eigenvalues on the alcoves $$A:=\{x\in\mathbb R^N| \> -1\leq x_1\le ...\le x_N\leq 1\}.$$ For $(k_1,k_2,k_3)=\kappa\cdot (a,b,1)$ with $a,b>0$ fixed, we derive a central limit theorem for the distributions above for $\kappa\to\infty$. The drift and the inverse of the limit covariance matrix are expressed in terms of the zeros of classical Jacobi polynomials. We also rewrite the CLT in trigonometric form and determine the eigenvalues and eigenvectors of the limit covariance matrices. These results are related to corresponding limits for $\beta$-Hermite and $\beta$-Laguerre ensembles for $\beta\to\infty$ by Dumitriu and Edelman and by Voit., Comment: The presentation of the results is improved, and additional references are added

The purpose of this work is to provide and analyzed the approximate analytical solutions for certain systems of fractional initial value problems (FIVPs) under the time-Caputo fractional derivatives by means of a novel attractive algorithm, called the Laplace residual power series (LRPS) algorithm. It combines the Laplace transform operator and the RPS algorithm. The proposed algorithm produces the fractional series solutions in the Laplace space based upon basically on the limit concept and then transforming bake them to original spaces to get a rapidly convergent series approximate solution. To validate the efficiency, accuracy, and applicability of the proposed algorithm, two illustrative examples are performed. Obtained solutions are simulated graphically and numerically. The analysis of results reached shows that the proposed algorithm is applicable, effective, and very fast in determining the solutions for many fractional problems arising in the various areas of applied mathematics

An analog of the First Szegő Limit Theorem for multiplicative Toeplitz operators is discussed, with the emphasis on the role of the multliplicative Følner condition in this topic.

Selecting the optimal venue for limit order placement depends on the specific exchanges competing at the NBBO at the time of order placement. The speed of a fill at NASDAQ depends not only on NASDAQ’s market share, but whether orders at the same price are also posted at IEX or EDGX, for example, or some other combination of the fifteen other exchanges—and 65,535 possible combinations of exchanges that could be competing simultaneously at the NBBO. This paper outlines specific examples of “queue-jumping” and describes quantitative methods that can be used to identify the exchanges with the highest likelihood of filling limit orders in real time. A ranking system called ELO used to rank chess players and online video gamers is applied; rankings are assigned to exchanges and used to determine which exchange is most likely to receive the next marketable order for any of the possible combinations in competition. Exchanges are ranked under varying conditions and the rankings are used to address the problem of queue-jumping. Key Findings ▪ Execution algorithms’ limit order routing infrastructure is often based on heuristics rather than empirical analysis of competitive passive fill rate and speed at each venue. This inefficiency and market fragmentation create opportunities for “queue-jumping”—execution of limit orders before those placed at an earlier time. Queue-jumping strategies can be used to improve algorithms’ passive fill rate and/or speed. ▪ The ELO method developed for ranking chess players is applied to US equity exchanges to aid in making decisions about where to post limit orders to best jump the queue and increase an algorithm’s passive fill rate and/or speed. ELO allows for a simple list of exchange rankings per stock but is not suitable for aggregation across stocks. ▪ A conditional fill rate matrix (the “WinMatrix”) is also applied for ranking exchanges, providing a relative likelihood of fill given that a particular exchange has a limit order present at the National Best Bid (NBB) or National Best Offer (NBO). The WinMatrix can be created for individual stocks or groups of stocks.

The (2 + 1)-dimensional generalized Bogoyavlensky-Konopelchenko equation is a significant physical model. By using the long wave limit method and confining the conjugation conditions on the interrelated solitons, the general M-lump, high-order breather, and localized interaction hybrid solutions are investigated, respectively. Then we implement the numerical simulations to research their dynamical behaviors, which indicate that different parameters have very different dynamic properties and propagation modes of the waves. The method involved can be validly employed to get high-order waves and study their propagation phenomena of many nonlinear equations.

This paper experimentally investigates the influence of working conditions on the friction properties, wear behaviors, and seizure limit of journal bearing friction pairs including the aluminum bronze shafts and the steel bearings. The tribological tests were conducted by the journal bearing friction and lubrication characteristic test-rig under different relative clearances, applied loads, rotational speeds, and inlet oil temperatures. The worn surfaces were measured by scanning electron microscopy, energy-dispersive X-ray spectroscopy, and laser microscopic 3D profile device to obtain the fault mechanisms. The results showed that the seizure limit value could be improved with the increase of relative clearance. The main wear mechanism of friction pairs is adhesive wear for a small relative clearance, and the main wear mechanism is transformed into abrasive wear with the increase of the bearing relative clearance.

This study aims to propose state-of-the-art techniques in predicting and controlling slope stability in open-pit mines based on limit equilibrium analysis, artificial neural networks, and optimization algorithms. Accordingly, the simplified Bishop method was used to analyze the slope stability of an open-pit coal mine through the limit equilibrium analysis method. Various rock mass properties and the geometrical parameters of the slopes were considered, such as bench height, slope angle, unit weight, cohesion, and friction angle. Finally, 495 cases were analyzed to compute the factor of safety (FOS). Subsequently, the radial basis function neural network (RBFNN) model was applied to predict FOS. In order to optimize the RBFNN model, the brainstorm optimization (BSO) algorithm was applied to train the RBFNN model, named as BSO-RBFNN model. The genetic algorithm (GA)-RBFNN, RBFNN (without optimization), and multiple layers perceptron (MLP) neural network were also developed to predict FOS and compared with the proposed BSO-RBFNN model as part of the study. The results revealed that the optimization of the BSO algorithm and RBFNN model provided a state-of-the-art technique (i.e., BSO-RBFNN) for predicting and controlling slope stability with high accuracy (i.e., mean absolute error (MAE) = 0.047, root-mean-squared error (RMSE) = 0.057, determination coefficient (R2) = 0.929, variance accounted for (VAF) = 92.948), and reliability (i.e., absolute error of 5.89% for 80% of cases in practice). Comparisons also indicated that the proposed BSO-RBFNN model is the most dominant model for predicting slope stability in this study (i.e., MAEGA-RBFNN = 0.048, RMSEGA-RBFNN = 0.060, R2GA-RBFNN = 0.927, VAFGA-RBFNN = 92.534; MAERBFNN = 0.064, RMSERBFNN = 0.081, R2RBFNN = 0.925, VAFRBFNN = 89.189; MAEMLP = 0.065, RMSEMLP = 0.081, R2MLP = 0.873, VAFMLP = 85.724). Furthermore, the slope angle and bench height should be taken into account to control slope stability in practical engineering based on the proposed BSO-RBFNN model.

The paper deals with the limit behavior of a compound Poisson process with switching between a finite number of sequences of i.i.d. random variables. The switching is provided by Bernoulli’s random variables. Under suitable normalization, the limit process is a Brownian motion with switching variance.

We introduce notions of generalized $$\varepsilon $$ -quasi solutions to approximate set type solutions of set optimization problems. We study their properties, consistency and limit behavior as approximations to efficient and strict weak efficient solutions. Moreover, we prove an existence result for such solutions and a bound for their asymptotic cone. Finally, we obtain optimality conditions for them.

We prove a limit theorem on the convergence of mathematical expectations of functionals of sums of independent random variables to the Cauchy problem solution for the nonstationary Schr¨odinger equation with a symmetric fractional derivative operator of order $$ \upalpha\ \upepsilon \bigcup_{m=3}^{\infty}\left(m-1,m\right) $$ in the righthand side.

The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a job is determined by the processing time of its first operation. At any point in time, the total consumption of this additional resource cannot exceed a given limit (referred to as the storage capacity). The goal is to minimise the makespan, i.e. to minimise the time needed for the completion of all jobs. This problem is NP-hard in the strong sense. The paper analyses how the parameter - a lower bound on the storage capacity specified in terms of the processing times, affects the computational complexity.

In this paper, forming limit diagram (FLD) of aluminum/brass two-layer sheets through an incremental forming process (ISF) was studied numerically and experimentally. At first, the two-layer aluminum 1050/brass (65% copper) sheets were fabricated using the roll bonding process. Also, the finite element simulations of the incremental forming process with ABAQUS software were utilized to predict the FLD. For this purpose, the criterion of the second derivative of the equivalent plastic strain was used to predict fracture. Finally, the numerical simulation results were compared with the experimental results. For instance, comparing experimental and numerical FLD0 values for the formed samples with forming angle 62.5-degree showed a 7% difference. However, the difference was negligible, and numerical simulation results could be used with an appropriate reliability coefficient. The effect of sheet arrangement towards tools was then investigated. It finds out from the experimental results that the formability of the Brass/Al (brass was up layer and aluminum was bottom layer) was more than the Al/Brass (aluminum is up layer and brass is bottom layer). In the following, the ISF parameters such as forming limit angle, step-down, and thickness distribution were investigated.

We present a unified approach to obtain sharp mean-squared and multiplicative inequalities of Hardy-Littlewood-Polya and Taikov types for multiple closed operators acting on Hilbert space. We apply our results to establish new sharp inequalities for the norms of powers of the Laplace-Beltrami operators on compact Riemannian manifolds and derive the well-known Taikov and Hardy-Littlewood-Polya inequalities for functions defined on the d-dimensional space in the limit case. Other applications include the best approximation of unbounded operators by linear bounded ones and the best approximation of one class by elements of another class. In addition, we establish sharp Solyar type inequalities for unbounded closed operators with closed range.

In this paper, meant as a companion to arXiv:2006.04458, we consider a class of non-integrable $2D$ Ising models in cylindrical domains, and we discuss two key aspects of the multiscale construction of their scaling limit. In particular, we provide a detailed derivation of the Grassmann representation of the model, including a self-contained presentation of the exact solution of the nearest neighbor model in the cylinder. Moreover, we prove precise asymptotic estimates of the fermionic Green's function in the cylinder, required for the multiscale analysis of the model. We also review the multiscale construction of the effective potentials in the infinite volume limit, in a form suitable for the generalization to finite cylinders. Compared to previous works, we introduce a few important simplifications in the localization procedure and in the iterative bounds on the kernels of the effective potentials, which are crucial for the adaptation of the construction to domains with boundaries., 69 pages. Minor revisions. Version accepted by Annales Henri Poincar\'e. arXiv admin note: substantial text overlap with arXiv:2006.04458

We consider a model whereby a given response variable Y following a transformation $${{\mathcal {Y}}}:=\mathcal {T}(Y)$$ , satisfies some classical regression equation. In this transformation model the form of the transformation is specified analytically but incorporates an unknown transformation parameter. We develop testing procedures for the null hypothesis of homoskedasticity for versions of this model where the regression function is considered either known or unknown. The test statistics are formulated on the basis of Fourier-type conditional contrasts of a variance computed under the null hypothesis against the same quantity computed under alternatives. The limit null distribution of the test statistic is studied, as well as the behaviour of the test criterion under alternatives. Since the limit null distribution is complicated, a bootstrap version is suggested in order to actually carry out the test procedures. Monte Carlo results are included that illustrate the finite-sample properties of the new method. The applicability of the new tests on real data is also illustrated.

Predictions of future water resources are essential for the strategic plans of any country especially in arid regions such as Saudi Arabia (SA). This paper presents a modeling study of the temporal annual rainfall variability over SA, evaluating the best model for future rainfall predictions and mapping spatiotemporal rainfall over SA. Common time series models of orders p and q such as autoregressive, AR(p), moving average, MA(q), and the combined autoregressive-moving average, ARMA(p,q), models are utilized. The models are applied to 28 metrological stations distributed over SA. Spatiotemporal statistical analysis of rainfall data is performed over a period between 1970 and 2012. The minimum and maximum fitted parameters of the models are φ1 = − 0.55, 0.46 for ARMA (1,0), θ1 = − 0.66, 0.17 for ARMA (0,1) and φ1 = − 0.84, 0.94, θ1 = − 0.87, 0.78 for ARMA (1,1), respectively. It has been shown that ARMA (1,0) is the best to model the temporal variability based on the Akaike information criterion (AIC), the correlation coefficient (R), and the root mean square error (RMSE). The Monte Carlo method is used to make future predictions (100 realizations) with the confidence levels (CIs) based on ARMA (1,0). Spatial distribution of the ensemble predictions and their CIs are presented graphically at the upper limit of 95%, 97.5%, and 99% and the lower limit of 5%, 2.5%, and 1% confidence, respectively, for the year 2030 to help decision-makers for future water resources planning of the country. Abha city has the highest annual rainfall prediction in 2030 (221 mm) with upper confidences (436, 533, and 643 mm) for 95%, 97.5%, and 99%, respectively. The prediction results indicate that the high mountainous areas (Asir and Taif) are expected to have more rainfall in the future than the rest of the regions in SA. The use of non-traditional water resources is the solution to future challenges.