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In the paper, a survey of the main results concerning univariate and multivariate exponential power (EP) distributions is given, with main attention paid to mixture representations of these laws. The properties of mixing distributions are considered and some asymptotic results based on mixture representations for EP and related distributions are proved. Unlike the conventional analytical approach, here the presentation follows the lines of a kind of arithmetical approach in the space of random variables or vectors. Here the operation of scale mixing in the space of distributions is replaced with the operation of multiplication in the space of random vectors/variables under the assumption that the multipliers are independent. By doing so, the reasoning becomes much simpler, the proofs become shorter and some general features of the distributions under consideration become more vivid. The first part of the paper concerns the univariate case. Some known results are discussed and simple alternative proofs for some of them are presented as well as several new results concerning both EP distributions and some related topics including an extension of Gleser’s theorem on representability of the gamma distribution as a mixture of exponential laws and limit theorems on convergence of the distributions of maximum and minimum random sums to one-sided EP distributions and convergence of the distributions of extreme order statistics in samples with random sizes to the one-sided EP and gamma distributions. The results obtained here open the way to deal with natural multivariate analogs of EP distributions. In the second part of the paper, we discuss the conventionally defined multivariate EP distributions and introduce the notion of projective EP (PEP) distributions. The properties of multivariate EP and PEP distributions are considered as well as limit theorems establishing the conditions for the convergence of multivariate statistics constructed from samples with random sizes (including random sums of random vectors) to multivariate elliptically contoured EP and projective EP laws. The results obtained here give additional theoretical grounds for the applicability of EP and PEP distributions as asymptotic approximations for the statistical regularities observed in data in many fields.

We consider the conditions for a finite set with a given system of operations (a finite algebra) to be subject to a probability limit theorem, i.e., arbitrary computations with mutually independent random variables have value distributions that tend to a certain limit (limit law) as the number of random variables used in the computation grows. Such behavior may be seen as a generalization of the central limit theorem that holds for sums of continuous random variables. We show that the existence of a limit probability law in a finite algebra has strong implications for its set of operations. In particular, with some geometric exceptions excluded, the existence of a limit law without zero components implies that all operations in the algebra are quasigroup operations and the limit law is uniform. [ABSTRACT FROM AUTHOR]

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Dunbar's number is the cognitive limit of an individual to maintain stable relationships with others in his network. It is based on the size of the neocortex of the human brain. On the other hand, trust is one of the major issues for one while selecting members for his social network and the evolution of his social network with time. Trust and Dunbar's number are interconnected in the case of one's stable social network. Trust needs time to be built after several social interactions, intimacy, etc. In this paper, we try to provide answers to the following important questions related to social networks: (i) Do trust levels remain the same for individuals from one's perspective in his social network when the network size increases? (ii) What is the relation between the power-law exponent α and the trust cutoff? (iii) Do trust levels help to diffuse information quickly or vice versa to reach Dunbar's number 150 along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes? We find that there is a requirement for trust levels to increase among the same individuals in one's social network if the size of the network increases. As a relation between the power-law exponent α and the trust cutoff, it is found that α ∝ 1/(trust cutoff). Moreover, we also find that trust levels never help to diffuse information quickly or vice versa to reach Dunbar's number 150, along with hierarchy layers of 5, 15, and 50 individuals in networks of different sizes., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Authors. Published by Elsevier Ltd.)

The Prufer angle is an effective tool for studying Sturm-Liouville problems and p-Laplacian eigenvalue problems. In this article, we show that for the p-Laplacian eigenvalue problem, when x is irrational in (0,1), a sequence of modified Prufer angles (after modulo $\pi_p$) is equidistributed in $(0,\pi_p)$. As a function of x, $\psi_n$ is also asymptotic to the uniform distribution on $(0,\pi_p)$.

Abstract In this work, we report an improved catalyst which is superior to known heterogeneous catalysts for dehydrocoupling of dimethylamine-borane (DMAB). The prepared three metallic nanocomposites consist of graphene oxide supported monodisperse palladium, ruthenium and nickel nanomaterials (3.78 ± 0.43 nm). The monodisperse PdRuNi nanoparticles decorated with graphene oxide (PdRuNi@GO) were synthesized according to the microwave synthesis method and characterized by TEM (Transmisson Electron Microscopy), HR-TEM (High Resolution Transmisson Electron Microscopy), XPS (X-ray photoelectron spectroscopy), XRD (X-ray diffraction) and Raman spectroscopy. The prepared trimetallic nanocomposites have shown outstanding performance and stability as a catalyst for the dehydrocoupling of dimethylamine-borane. To the best of our knowledge, the prepared monodisperse PdRuNi@GO nanoparticles have one of the best catalysts with outstanding TOF (Turnover Frequency) value (737.05 1/h) and E a (55.47 kJ/mol) (activation energy) among all catalysts prepared for dehydrogenation of dimethylamine-borane at low temperatures. Highlights • Highly monodisperse trimetallic PdRuNi nanocomposites decorated on graphene oxide. • The synthesis of PdRuNi@GO by using microwave-assisted polyol method. • The discovery of a remarkable DMAB dehydrocoupling catalyst. • The record TOF value of PdRuNi@GO for dimethylamine−borane dehydrogenation. • The ultrasmall sizes and high metallic ratio of PdRuNi@GO nanocomposites. [ABSTRACT FROM AUTHOR]

The expected distortion decrease per bit attained by conveying the significance and refinement information of transform coefficients is derived taking into consideration their Probability Distribution Function (PDF) and their entropy. A general scheme for finding the static rate–distortion optimized ordering for the bits of the coefficients for all subbands of a generic N -level dyadic biorthogonal Discrete Wavelet Transform (DWT) is given by weighting their distortion decrease per bit using the gain of each decomposition subband. Specific formulation for the Exponential Power Distribution (EPD) family is given and closed formulae are derived for the special cases of the Uniform and Laplace distributions. It is shown that under certain circumstances some refinement information of larger magnitude coefficients should be conveyed before the significant information of the current ones. The results can be applied by both conventional context modeling entropy coding algorithms or by set-partitioning algorithms which use multiple lists to keep track of significant and refinement coefficients. A very fast set-partitioning compression algorithm (Depth Embedded Block Tree — DEBT) has been developed based on variable-depth blocks and trees which uses the results presented here and achieves excellent compression ratios along with many other desired properties, e.g., embedded rate–distortion optimized lossy or lossless stream, quality or resolution scalability, and region of interest, among others. Tests show that the rate–distortion curves of most images show a significant improvement when using the weighting derived by the appropriate Exponential Power Distribution fitting in comparison to using a priori standard Uniform or Laplace Probability Distribution Function when using a non orthogonal Discrete Wavelet Transform. [ABSTRACT FROM AUTHOR]

In many applications we are faced with the problem of estimating object dimensions from a noisy image. Some devices like a fluorescent microscope, X-ray or ultrasound machines, etc., produce imperfect images. Image noise comes from a variety of sources. It can be produced by the physical processes of imaging, or may be caused by the presence of some unwanted structures (e.g. soft tissue captured in images of bones). In the proposed models we suppose that the data are drawn from uniform distribution on the object of interest, but contaminated by an additive error. Here we use two one-dimensional parametric models to construct confidence intervals and statistical tests pertaining to the object size and suggest the possibility of application in two-dimensional problems. Normal and Laplace distributions are used as error distributions. Finally, we illustrate ability of the R-programs we created for these problems on a real-world example. [ABSTRACT FROM AUTHOR]

Distribution laws and confidence limits are derived for the relative error of a complex measuring channel that contains several simple measuring channels. Calculations are performed with the assumption that the error of each simple measuring channel has uniform distribution on a specified section. It is shown that divergences of the values of the relative errors calculated for the composite error distribution of the complex measuring channel and for the normal distribution with the same value of dispersion do not exceed 3%, with a confidence probability of P = 0.95. [ABSTRACT FROM AUTHOR]

A sum sequence modulo n is a sequence S = ( s 1 , s 2 , … , s d ) of elements in Z / n Z such that every x ∈ Z / n Z can be represented as s i + s j , i < j , in the same number λ of ways. For example, ( 0 , 1 , 2 , 4 ) is a sum sequence modulo 6 with λ = 1 . We examine polynomials associated with sum sequences using tools from number theory, combinatorics and Galois theory. In particular, we give a complete characterization of sum sequences and their associated polynomials. We also describe some variations on these ideas and mention several possible generalizations to arbitrary finite groups. [ABSTRACT FROM AUTHOR]

Abstract: Independent component analysis plays a central role in blind source separation, leading to many applications of signal processing such as telecommunications, speech processing, and biomedical signal processing. Although the independent component analysis requires cost functions for evaluation of mutual independence of observed signals, little has been reported on theoretical investigation of the characteristics of such cost functions. In this paper, we mathematically analyze the cost function based on Kullback–Leibler divergence in independent component analysis. Our analysis proves that the cost function becomes unimodal when the number of source signals is two and both of the source signals have uniform distributions. In order to derive this result, we make use of whitening of observed signals and we describe the cost function in closed form. [ABSTRACT FROM AUTHOR]

Although the law of the iterated logarithm for discrepancies of geometric progression is proved, the constants appearing there are not concretely evaluated for small ratios. We consider the case when the ratio is a power root of a small rational number, and make a conjecture on the concrete value of the constant. We give several examples which are consistent with the conjecture. [ABSTRACT FROM AUTHOR]

We investigate the optimality of adaptive importance sampling by stochastic approximation. To address the well-known difficulty in the implementation of stochastic approximation, that is, the extreme performance sensitivity to the choice of decreasing learning rates, we focus on constant learning rates for a finite computing budget, derived via minimization of an upper bound of the theoretical variance of the empirical mean, not via accelerated convergence of the objective function as in the existing stochastic gradient framework. Strong convexity of the objective function lowers the upper bound of the theoretical variance, while the convexity parameter is not required for implementation. In contrast to existing schemes based on sample average approximation, the proposed approach based on stochastic approximation has the potential to run reasonably robust adaptive importance sampling with significantly less computing cost. We provide numerical results to support the theoretical findings and to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We propose a new variable interval (VI) schedule that achieves constant probability of reinforcement in time while using a bounded range of intervals. By sampling each trial duration from a uniform distribution ranging from 0 to 2 T seconds, and then applying a reinforcement rule that depends linearly on trial duration, the schedule alternates reinforced and unreinforced trials, each less than 2 T seconds, while preserving a constant hazard function. [ABSTRACT FROM AUTHOR]

Arsenic element refines W powders significantly during the hydrogen reduction process of tungsten oxide in our previous studies. In this paper, the nanocrystalline WC-As composite powders were prepared by carbonization of nano W-As composite powders and the effects of arsenic on the growth of WC powder were discussed in detail. The prepared samples were characterized by X-ray diffraction, differential scanning calorimetric analysis, scanning electron microscope, transmission electron microscope, X-ray photoelectron spectroscopy and Inductively Coupled Plasma. The results showed that arsenic appropriately raised the initial temperature of carbonization, significantly accelerated carbonization reaction process and shorten the reaction time. Moreover, WC-As composite powders merged and grew up directly without particle expansion and cracking. And the nano WAs 2 particles attached to WC grain boundaries and hindered the growth of WC grain through grain boundary migration. The above two effects resulted in the WC-As composite powders prepared at 1300 °C for 2 h with the average size of about 121 nm in diameter. [ABSTRACT FROM AUTHOR]

In recent years, computer science specialists are faced with the challenge of processing massive amounts of data. To overcome this barrier, researchers have developed new techniques to process data in efficient ways. This paper aims to present an algorithm for sorting uniformly distributed numbers, called Unisort. Given a uniformly distributed array of numbers, the algorithm places the numbers into bins to obtain sorted sub-arrays. It then merges the sorted sub-arrays to obtain the final sorted array. This work demonstrates that if numbers are uniformly distributed, the algorithm is able to sort them in O(n) time. Furthermore, the algorithm can be generalized to numbers produced by any known distribution. The only requirement is to know the distribution a priori. However, in the worst case scenario, when the distribution is not known, the numbers may fall in the same bin. For the worst case, the algorithm becomes similar to merge sort. Experiments conducted to assess the performance level of the algorithm, in terms of time efficiency, show that it is faster than quicksort, heapsort and Bucket sort. The algorithm has broad applications in information technology, since almost every information system organizes data by sorting it. [ABSTRACT FROM AUTHOR]

Distribution characteristics of diamond particles affect the grinding performance of grinding wheel in precision and ultra-precision grinding. In fact, distribution of diamond particles is un-uniform in most grinding wheels. A method for achieving uniform distribution of diamond particles by electrostatic spraying is proposed in this paper. A long-time stable diamond particle suspension is prepared by mixing kerosene and Tween80 mixture. Under different electrostatic voltage, there are three spraying modes including droplet mode, cone-jet mode, and multi-jet model. The influences of voltage, flow rate, and collection distance on the uniformity, distribution density, and distribution range of diamond particles are discussed. The diamond particles are counted by image processing including binarization, mesh partition, and particle counting. The experimental results have shown that the uniform distribution of diamond particles can be achieved by using electrostatic spraying method. In the conditions of voltage 6 kV, flow rate 5 mL/h, and collection distance 30 mm, a distribution deviation of 0.11 can be obtained. It is expected that this work will contribute to fabricating the high-performance grinding wheel with uniform diamond particles. [ABSTRACT FROM AUTHOR]

In this paper, we compare the performance of Distributed Coordination Function (DCF) and Enhanced Distributed Channel Access (EDCA) for normal and uniform distributions of mesh clients considering two Wireless Mesh Network (WMN) architectures. As evaluation metrics, we consider throughput, delay, jitter and fairness index metrics. For simulations, we used WMN-GA simulation system, ns-3 and Optimized Link State Routing. The simulation results show that for normal distribution, the throughput of I/B WMN is higher than Hybrid WMN architecture. For uniform distribution, in case of I/B WMN, the throughput of EDCA is a little bit higher than Hybrid WMN. However, for Hybrid WMN, the throughput of DCF is higher than EDCA. For normal distribution, the delay and jitter of Hybrid WMN are lower compared with I/B WMN. For uniform distribution, the delay and jitter of both architectures are almost the same. However, in the case of DCF for 20 flows, the delay and jitter of I/B WMN are lower compared with Hybrid WMN. For I/B architecture, in case of normal distribution the fairness index of DCF is higher than EDCA. However, for Hybrid WMN, the fairness index of EDCA is higher than DCF. For uniform distribution, the fairness index of few flows is higher than others for both WMN architectures. [ABSTRACT FROM AUTHOR]

In order to improve the overall efficiency of cascade hydropower stations and obtain optimum scheduling scheme, the optimal scheduling model of cascade hydropower stations was established based on Particle Swarm Algorithm Catfish Effect. For the limitation of falling into local acceleration easily of Catfish Effect on Particle Swarm Optimization (CE-PSO) when making catfish particles, it believed that the spatial distribution position of particles catfish had an important impact on improving the diversity of particles. Therefore, catfish particles were tried to uniformly distribution throughout the search space aiming to improve search efficiency and make up the limitation of CE-PSO to fall into the local acceleration. The improved algorithm was applied to the optimal scheduling of cascade hydropower stations in a certain river and the results show that the improved CE-PSO has a certain degree of improvement in the global search ability and convergence speed compared with standard PSO and CE-PSO. The results have a positive effect on improving the efficiency of cascade hydropower stations and obtaining optimum scheduling scheme of power plants. [ABSTRACT FROM AUTHOR]

Let ζsQ be the Epstein zeta-function associated with an integral quadratic form Qy=ytQy for y ϵ ℤn with nontrivial zeros ρ = β + iy. We prove that Σγ for all Epstein zeta functions analogously to Landau’s explicit formula in the case of the Riemann zeta function. It follows that under the assumption Σγ where NTQ counts the nontrivial zeros for |γ| < T, the ordinates of Epstein zeta zeros are uniformly distributed modulo one. [ABSTRACT FROM AUTHOR]

Power flow studies are very important and are essential for fault analysis and stability analysis. Conventional Newton-Raphson-based power flow analysis is for fixed loads and generations. However, load and generation powers are uncertain due to factors like forecasting error, sudden outages, etc. Monte Carlo was widely used for power flow analysis with uncertainty. Due to excessive computational time involved in Monte Carlo, affine arithmetic-based power flow analysis was introduced. In the present work, a modified affine arithmetic-based power flow analysis is proposed. The proposed method needs less computational memory and gives tighter bounds on voltage magnitudes and angles of the system buses for a given uncertainty range of load and generation powers as compared to existing affine arithmetic-based power flow analysis. The proposed method is implemented on IEEE 30 and IEEE 118 bus systems and detailed simulation results are presented. The results are compared with Monte Carlo simulations as well as existing affine arithmetic-based power flow analysis. The results show that the proposed modified affine arithmetic-based power flow analysis yields more accurate solution intervals for voltage magnitude, voltage angles, real, and reactive power flows as compared to existing affine arithmetic-based power flow analysis. [ABSTRACT FROM AUTHOR]

Microspheres coated with specific biomolecules have been broadly employed to detect tumor markers. In this study, we developed a novel microfluidic platform based on pressure difference for the uniform distribution of microspheres and applied this platform for carcinoma-embryonic antigen detection with quantum dots probes. Within our microfluidic device, micropost arrays were designed to ensure that the trapped microspheres formed dot arrays to overcome the shortcomings of clogging and loss of microspheres, which typically occurred in currently used structures for microsphere capture. A sandwich immunoassay for the detection of typical cancer biomarker CEA was successfully performed on the microfluidic device with all reagents reacted together, which led to reduced experimental time and simple operations. As a result, a limit of detection of 0.5 ng/mL for carcinoma-embryonic antigen detection was achieved, and the calibration curve fitted the Langmuir model, which showed high clinical consistency with serum sample detection. To further investigate the performance of our system, trap efficiency and uniform ratio of microfluidic structure, and specificity of the experiment were evaluated and showed good consequences. The proposed microfluidic immunoassay system with advantages of high sensitivity and specificity, reduced time cost, and facile operations, indicates a promising potential in clinical diagnosis. [ABSTRACT FROM AUTHOR]

We study the notion of van der Corput sets with respect to general compact groups. [ABSTRACT FROM AUTHOR]

Achieving a uniform distribution of zinc in the negative electrode is crucial to increase the electrode utilization, maximize the discharge capacity, suppress the dendrite formation and enhance the cycling stability for zinc bromine flow batteries (ZBFBs). To promote the uniform distribution of zinc and thus propel the commercial applications for ZBFBs, in this work, a first-principles study is carried out to investigate the zinc adsorption and diffusion on representative carbon surfaces, including a pristine graphite (0 0 0 1) surface, two surfaces with vacancies, and three surfaces with oxygen-functional groups, aiming to unravel the effect of carbon defects on the ion transport inside the porous electrode, clarify the underlying zinc anchoring mechanism and seek effective ways to promote the uniform distribution of zinc. It is found that the zinc distribution and morphology can be varied by adjusting carbon surface properties, especially by increasing the number of single vacancy. A graphite felt negative electrode with a high content of carbon defects is then prepared and tested in ZBFBs. Experimental results reveal that a much more uniform distribution of zinc is achieved in the prepared electrode than the original electrode does after charing, demonstrating the validity of our proposed mechanism and method. The results reported here provide new insights and novel methods to fabricate uniformly distributed zinc negative electrode, which can guide the rational design of electrode and promote the future applications of ZBFBs and other hybrid flow batteries ( e.g. Zn-I 2 , Zn-Ce and all-iron). [ABSTRACT FROM AUTHOR]

In this study, we present a design methodology that enables the automation of cell culture using a fluidic bioreactor module in a uniform, massively parallel fashion. To demonstrate our proof-of-concept validation, we designed the channel lengths that can uniformly distribute the fluid from one inlet to two to the power of n outlets. In our experiments, the module was composed of four layers which can hold eight petri dishes on each layer. The channel outlets were connected to the petri dishes, respectively. Cells and media were distributed into each petri dish by compensating the channel lengths with different potential energy of each layer in a controlled manner. The results show that the module was well-designed for the parallel supply of medium in automatic cell culture. Overall, the process can be automated by controlling the on/off events temporally, such as injecting a new cell media and removing the waste. [ABSTRACT FROM AUTHOR]

In 2009, the Commission on Isotopic Abundances and Atomic Weights (CIAAW) of the International Union of Pure and Applied Chemistry (IUPAC) introduced the interval notation to express the standard atomic weights of elements whose isotopic composition varies significantly in nature. However, it has become apparent that additional guidance would be helpful on how representative values should be derived from these intervals, and on how the associated uncertainty should be characterized and propagated to cognate quantities, such as relative molecular masses. The assignment of suitable probability distributions to the atomic weight intervals is consistent with the CIAAW's goal of emphasizing the variability of the atomic weight values in nature. These distributions, however, are not intended to reflect the natural variability of the abundances of the different isotopes in the earth's crust or in any other environment. Rather, they convey states of knowledge about the elemental composition of "normal" materials generally, or about specific classes of such materials. In the absence of detailed knowledge about the isotopic composition of a material, or when such details may safely be ignored, the probability distribution assigned to the standard atomic weight intervals may be taken as rectangular (or, uniform). This modeling choice is a reasonable and convenient default choice when a representative value of the atomic weight, and associated uncertainty, are needed in calculations involving atomic and relative molecular masses. When information about the provenance of the material, or other information about the isotopic composition needs to be taken into account, then this distribution may be non-uniform. We present several examples of how the probability distribution of an atomic weight or relative molecular mass may be characterized, and also how it may be used to evaluate the associated uncertainty. [ABSTRACT FROM AUTHOR]

Particle swarm optimization (PSO) algorithm is generally improved by adaptively adjusting the inertia weight or combining with other evolution algorithms. However, in most modified PSO algorithms, the random values are always generated by uniform distribution in the range of [0, 1]. In this study, the random values, which are generated by uniform distribution in the ranges of [0, 1] and [-1, 1], and Gauss distribution with mean 0 and variance 1 (U[0, 1], U[-1, 1] and G(0, 1)), are respectively used in the standard PSO and linear decreasing inertia weight (LDIW) PSO algorithms. For comparison, the deterministic PSO algorithm, in which the random values are set as 0.5, is also investigated in this study. Some benchmark functions and the pressure vessel design problem are selected to test these algorithms with different types of random values in three space dimensions (10, 30, and 100). The experimental results show that the standard PSO and LDIW-PSO algorithms with random values generated by U[-1, 1] or G(0, 1) are more likely to avoid falling into local optima and quickly obtain the global optima. This is because the large-scale random values can expand the range of particle velocity to make the particle more likely to escape from local optima and obtain the global optima. Although the random values generated by U[-1, 1] or G(0, 1) are beneficial to improve the global searching ability, the local searching ability for a low dimensional practical optimization problem may be decreased due to the finite particles. [ABSTRACT FROM AUTHOR]

A uniformly random ray pattern matrix A with a given zero-nonzero pattern (described by a digraph D with no multi-arcs or loops) is the matrix whose nonzero entries are mutually independent random variables uniformly distributed over the unit circle S 1 in the complex plane. It is shown in this paper that the probability of I − A to be ray nonsingular is completely determined by the cycle graph CG ( D ) of D (i.e. the adjacency structure of the directed cycles in D ) if CG ( D ) is a tree. A formula is given to compute the probability when CG ( D ) is a tree, and it is also shown that as the order of CG ( D ) tends to infinity, the limit of the probability is 0. [ABSTRACT FROM AUTHOR]

Exact confidence intervals for each of the endpoints a and b of the uniform distribution on the interval [a, b] with unknown a and b, as well as an exact confidence rectangle for the pair (a, b), are given. [ABSTRACT FROM AUTHOR]

Here we consider melting of an ultrathin lubricant layer between two atomically smooth solid surfaces taking into account the stress dependence of the lubricant shear modulus and its decrease with increasing stress (strain). In the adiabatic approximation with the stress relaxation time far longer than strain and temperature relaxation times, a Langevin equation is written and its respective Fokker-Planck equation is derived using the Stratonovich calculus. Phase diagrams for the steady case are presented illustrating the effect of the system parameters on the lubricant behavior. A joint numerical and analytical analysis demonstrates a very close match between probability distributions at different parameters. It is shown that in a limited stress range, a self-similar mode of dry friction is established showing up in self-similar behavior of stress time series. [ABSTRACT FROM AUTHOR]

We prove that, for arbitrary Dirichlet L-functions $$L(s;\chi _1),\ldots ,L(s;\chi _n)$$ (including the case when $$\chi _j$$ is equivalent to $$\chi _k$$ for $$j\ne k$$ ), suitable shifts of type $$L(s+i\alpha _jt^{a_j}\log ^{b_j}t;\chi _j)$$ can simultaneously approximate any given set of analytic functions on a simply connected compact subset of the right open half of the critical strip, provided the pairs $$(a_j,b_j)$$ are distinct and satisfy certain conditions. Moreover, we consider a discrete analogue of this problem where t runs over the set of positive integers. [ABSTRACT FROM AUTHOR]

The Lottery has attracted a lot of people with Fortune hopes. The games are relatively simple and, probably because of the millionaires awards has attracted the interest of many people. Games such as the Mega Sena in Brazil are good examples of probability distribution in an equiprobable space and allow the understanding of various aspects of statistical theories. In this work, a little analysis of the Mega Sena game is proposed, as well as analysis of the results of competitions already made. A hypothesis test is used to verify the equiprobable character of the game. [ABSTRACT FROM AUTHOR]

Hybrid aluminum matrix composites (HAMCs) are capable to meet recent demands of advanced engineering applications due to its tunable mechanical properties and lower cost. Stir casting is one of the prominent and economical method for processing of continuous reinforced HAMCs. In this method, flow pattern is the key factor for distribution of particles in the molten metal. Effective flow pattern can be achieved by optimizing stirring parameters i.e. blade angle, impeller size and stirring speed. However, complete study and optimization of flow is a challenge for research community. Finite element method simulation along with optimization technique is one of the effective combination to guide experimental research. In this paper, computational fluid dynamics has been used to simulate fluid flow during stir casting, whereas optimization of stirring parameters is done by Grey Taguchi method. Optimized parameters have been used for experimental synthesis of HAMCs. Furthermore, optical micrograph and hardness confirms about the uniform dispersion of reinforcements. These results may guide the researchers for the preparation of HAMCs with uniform particle distribution by stir casting route for industrial applications. [ABSTRACT FROM AUTHOR]