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We consider the orientational order that arises from the alignment of anisotropic biological cells confined in bounded domains. Especially, it is known that topological defects, where the orientation angles are not well-defined, play an important role in the global pattern formation of cell alignment. Hence, it is important to investigate the relationship between the shape of the region and the location of the defects. The orientational order of cells is theoretically modelled as a harmonic function achieving the minimum elastic energy state of the nematic liquid crystal, and an analytical formula in simply connected domains is given by Miyazako & Nara (Miyazako, Nara 2022 R. Soc. Open Sci. 9, 211663 (doi:10.1098/rsos.211663)). In this paper, we extend this study to construct an analytic formula of cell angle in the doubly connected domains, where topological defects and boundary shapes are represented as the positions of logarithmic singularities and as conformal maps from a given region to a standard annular region, respectively. In addition, using this analytical formula, we propose a numerical algorithm to minimize elastic energy, from which we investigate cell alignment in doubly connected domains with anisotropic quadrilateral boundaries. Our numerical simulations suggest that pairs of topological defects tend to be located around corners of the boundaries, which will be a design principle of the boundary geometry for controlling the defect positions and cell alignment. [ABSTRACT FROM AUTHOR]

Multi-cropping is becoming an increasingly popular technique in agriculture to tackle major and complex agroecosystem problems such as biodiversity and soil fertility loss, erosion and degradation, increased greenhouse gas emissions, etc. Comprehensively assessing the impact of multi-cropping intensity on agroecosystems is a new and still under-researched approach that can provide a better understanding of the impact of individual indicators on the overall functioning of biodiverse agroecosystems. Data from a stationary field experiment using multi-cropping at the Vytautas Magnus University Experimental Station between 2020 and 2022 were used to carry out this study. The study included maize, hemp, and faba bean as single, binary, and ternary crops. A complex assessment approach (CEI value) was used to determine the impact of these crops on the agroecosystem, the interrelationships between the main indicators, and the strength of their effects. It was found that the ternary maize–hemp–faba bean crop had the most positive effect on the agroecosystem. The effectiveness of other crops was 2 to 35% less. The lowest value was calculated for the maize–faba bean crop. [ABSTRACT FROM AUTHOR]

The pre-research data of mathematics prospective teachers in one of the universities in Bandung showed that the deductive reasoning ability in complex analysis was still not at good level. Beside the cognitive aspect, the affective aspect could be considered too in doing learning process, such as mathematical resilience. This study aims to analyze and identify the correlation between deductive reasoning and mathematical resilience in complex analysis. The research was conducted in one of the mathematics education departments of a university in Bandung. Correlation was the method used in this study. Mathematics prospective teachers were the sample of this research. This study concluded that mathematical deductive reasoning of prospective teachers was on a moderate level, the mathematical resilience of prospective teachers was on the positive category, and there was a significant correlation between deductive reasoning and the mathematical resilience of prospective teachers on a moderate level. [ABSTRACT FROM AUTHOR]

Deriving analytical expressions of dielectric permittivities is required for numerical and physical modeling of optical systems and the soar of non‐Hermitian photonics motivates their prolongation in the complex plane. Analytical models are based on the association of microscopic models to describe macroscopic effects. However, the question is to know whether the resulting Debye–Drude–Lorentz models are not too restrictive. Here, it is shown that the permittivity must be treated as a meromorphic transfer function that complies with the requirements of complex analysis. This function can be naturally expanded on a set of complex singularities. This singularity expansion of the dielectric permittivity allows to derive a generalized expression of the Debye–Drude–Lorentz model that complies with the requirements of complex analysis and the constraints of physical systems. It is shown that the complex singularities and other parameters of this generalized expression can be retrieved from experimental data acquired along the real frequency axis. The accuracy of this expression is assessed for a wide range of materials including metals, 2D materials and dielectrics, and it is shown how the distribution of the retrieved poles helps in characterizing the materials. [ABSTRACT FROM AUTHOR]

In this paper we study the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a real, positive, multi-humped, fairly smooth but not necessarily analytic potential decaying at infinity. We provide the rigorous semiclassical analysis of the Bohr-Sommerfeld condition for the location of the eigenvalues, the norming constants, and the reflection coefficient. [ABSTRACT FROM AUTHOR]

The article reveals linguocognitive mechanisms as well as social reasons for active functioning of new borrowings in the modern public discourse and in commercial enterprises naming. The material for the analysis is a sample of the most frequent lexis in the micro synchrony that are not yet part of the host language lexicon, and comprises over one hundred and fifty lexical units, selected from the national corpus of the Russian language, public internet discourse, the author’s collection of brand names (and names of businesses), radio and television programs. As a result of a comprehensive analysis, two main isomorphic types of borrowing functioning are identified. They are supposed to be motivated by multi-level linguistic, social, and pragmatic factors. Hence, the evidence of linguomental transformations of meaning is linked to the condition of linguistic frustration. This justifies considering it as a state of linguistic personality (at both the first and second levels, according to Yu.N. Karaulov), wherein the constraints of linguistic norms are lifted, and foreign-language word usage is motivated in specific speech act. A tendency of duplicate (native and foreign) naming in explicitly nominative and implicitly subjective-pragmatic functions has been established. It is suggested that the synergy of these functions conveys the speaker’s subjective intentions and can be regarded as a marketing strategy of self-positioning in the act of foreign-language use in the nomination process, or as a commercial move, emphasizing the value of the product / service (i.e., commercialization of the nominative unit). Thus, the discourse becomes either status-oriented or conative. The linguistic phenomena under consideration introduce changes into the national concept sphere, as they contain features of a different language world view.

Path planning for a point-mass robot moving in a cluttered two-dimensional environment is a well studied but non-trivial problem. In this paper we propose a novel computationally efficient and resolution-complete path generation method based on electrostatics. The proposed scheme comprises two stages. First, an auxiliary electrostatic problem is formulated where the boundary conditions of the Laplace equation are specified based on the map of the original path planning problem and is solved to obtain a map-specific electrostatic potential. Second, feasible paths are constructed by following any equipotential curve whose potential value is different from those of obstacles and boundaries. The electrostatic potential in the proposed method differs from the celebrated repulsive/attractive force-based potential field by its non-vanishing gradient, based on which the resolution-completeness is established. The computational efficiency of the proposed method arises from a novel electrostatic solver based on complex analysis, and on an original collision-checking algorithm inspired by the Residue theorem. Extensive numerical examples are provided to demonstrate the effectiveness and limitations of the proposed method. We believe this work provides an unconventional strategy for quantitatively encoding global map information and can play a role complementary to prevailing path planning methods.

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The main aim of this note is first to give the definition of the local classes. It also aims at studying the local property of some subclasses of plurisubharmonic functions by using these concepts. [ABSTRACT FROM AUTHOR]

A way is presented to design quantum wave functions that exhibit backflow, namely negative probability current despite having a strictly positive spectrum of momentum. These wave functions are derived from rational complex functions which are analytic in the upper half-plane and have zeros in the lower half-plane through which the backflowing behavior is controlled. In analogy, backflowing periodic wave functions are derived from rational complex functions which are analytic in the interior and have appropriately placed zeros or poles in the exterior of the unit circle. The concept is combined with a Padé-type procedure to design wave functions of this type that approximate a desired profile along the interval of backflow. It is finally shown that the time evolution of these wave packets is elegantly expressed in terms of the well-known Fresnel integrals. [ABSTRACT FROM AUTHOR]

The transition from Riemann integrals to other real integrals has been discussed previously in mathematics education literature. In this transition, the interpretation of integrals as averages of the integrated functions generalises smoothly to measure and probability theory. In this paper, I address the transition to complex path integrals. Based on the premise that using core ideas throughout mathematics curricula may facilitate the transition from earlier to more advanced courses, I analyse epistemologically to what extent the idea of averaging may be transferred to complex path integrals. In this case, the transition poses special epistemological challenges. Using an example from an expert interview, in which the expert aims to apply the interpretation of integrals as averages to complex path integrals, I illustrate the aforementioned challenges empirically. [ABSTRACT FROM AUTHOR]

This paper proposes a new methodology called TOpic modeling Based Index Assessment through Sentiment (TOBIAS). This method aims at modeling the effects of the topics, moods, and sentiments of the comments describing a phenomenon upon its overall rating. TOBIAS is built combining different techniques and methodologies. Firstly, Sentiment Analysis identifies sentiments, emotions, and moods, and Topic Modeling finds the main relevant topics inside comments. Then, Partial Least Square Path Modeling estimates how they affect an overall rating that summarizes the performance of the analyzed phenomenon. We carried out TOBIAS on a real case study on the university courses' quality evaluated by the University of Cagliari (Italy) students. We found TOBIAS able to provide interpretable results on the impact of discussed topics by students with their expressed sentiments, emotions, and moods and with the overall rating. [ABSTRACT FROM AUTHOR]

We take a look at weighted Szegő projections on ellipses and ellipsoids in light of some known results of real and complex potential theory. We show that on planar ellipses there is a weighted Szegő projection taking polynomials to polynomials without increasing degree. [ABSTRACT FROM AUTHOR]

• An analytical method solving SIFs of asymmetric circular and elliptical hole-edge cracks is proposed. • The impact of multiple interactive cracks on SIFs is studied. • Safe cracks tip distance is advised based on the reliability analysis of an engineering case. In this paper, a successive conformal mapping technique is used to propose an analytical method for solving the stress intensity factor (SIF) of asymmetrical hole-edge cracks on the basis of Muskhelishvili's complex variable function analysis method. Based on this analytical solution, the superposition method is used to get the SIF under the interaction of multiple cracks. Subsequently, according to the plastic collapse criterion, the residual strength under the interaction of two collinear asymmetric elliptical hole-edge cracks with different sizes on the side rail of a dumper's frame is analyzed through the method established. The failure probability of the plate part is obtained by the Kriging meta-model. This study provides a theoretical guide for the operation and maintenance plan of plate parts with multiple cracks. [ABSTRACT FROM AUTHOR]

The calculation of conformal mapping for irregular domains is a crucial step in deriving analytical and semi-analytical solutions for irregularly shaped tunnels in rock masses using complex theory. The optimization methods, iteration methods, and the extended Melentiev's method have been developed and adopted to calculate the conformal mapping function in tunnel engineering. According to the strict definition and theorems of conformal mapping, it is proven that these three methods only map boundaries and do not guarantee the mapping's conformal properties due to inherent limitations. Notably, there are other challenges in applying conformal mapping to tunnel engineering. To tackle these issues, a practical procedure is proposed for the conformal mapping of common tunnels in rock masses. The procedure is based on the extended SC transformation formulas and corresponding numerical methods. The discretization codes for polygonal, multi-arc, smooth curve, and mixed boundaries are programmed and embedded into the procedure, catering to both simply and multiply connected domains. Six cases of conformal mapping for typical tunnel cross sections, including rectangular tunnels, multi-arc tunnels, horseshoe-shaped tunnels, and symmetric and asymmetric multiple tunnels at depth, are performed and illustrated. Furthermore, this article also illustrates the use of the conformal mapping method for shallow tunnels, which aligns with the symmetry principle of conformal mapping. Finally, the discussion highlights the use of an explicit power function as an approximation method for symmetric tunnels, outlining its key points. [ABSTRACT FROM AUTHOR]

Results on the rational approximation of functions containing singularities are presented. We build further on the "lightning method," recently proposed by Trefethen and Gopal [SIAM J. Numer. Anal., 57 (2019), pp. 2074-2094], based on exponentially clustering poles close to the singularities. Our results are obtained by augmenting the lightning approximation set with either a low-degree polynomial basis or partial fractions with poles clustering toward infinity in order to obtain a robust approximation of the smooth behavior of the function. This leads to a significant increase in the achievable accuracy as well as the convergence rate of the numerical scheme. For the approximation of xα on [0, 1], the optimal convergence rate as shown by Stahl [Bull. Amer. Math. Soc., 28 (1993), pp. 116-122] is now achieved simply by least-squares fitting. [ABSTRACT FROM AUTHOR]

Idioms express emotional states, e.g., grief, anger, joy, sadness, fear, etc. However, they can also reveal the values, moral qualities, and directive potential of the speaker. This article reviews some existing approaches to phraseological studies and introduces an authentic comprehensive approach that covers syntactic, figurative, historical, axiological, and pragmatic levels. The material was obtained from film dialogues and analyzed from the communicative-pragmatic standpoint. The goal was to reveal the ethnic and cultural aspect of idiomatic expressions in Chinese cinema discourse. In the Chinese series 靠近你温暖我 (Close to You, Make Me Warm), the authors identified a number of idioms that explicated the following concepts: 独守空房 (dúshǒu kōngfáng) – Loneliness; 守身如玉 (shǒu shēn rú yù) – Honesty, 人算不如天算 (rénsuàn bùrú tiānsuàn) – Justice, 相亲相爱 (xiāngqīn xiāng’ài) – Love, 藕断丝连 (ǒu duàn sī lián) – Parting;白头偕老 (báitóu xiélǎo) – Marriage; 百闻不如一见 (bǎiwén bùrú yījiàn) – Trust; 两肋插刀 (liǎng lèi chā dāo) – Friendship. The new approach proved able to identify the value and pragmatics of phraseological units.

Multi-cropping is becoming an increasingly popular technique in agriculture to tackle major and complex agroecosystem problems such as biodiversity and soil fertility loss, erosion and degradation, increased greenhouse gas emissions, etc. Comprehensively assessing the impact of multi-cropping intensity on agroecosystems is a new and still under-researched approach that can provide a better understanding of the impact of individual indicators on the overall functioning of biodiverse agroecosystems. Data from a stationary field experiment using multi-cropping at the Vytautas Magnus University Experimental Station between 2020 and 2022 were used to carry out this study. The study included maize, hemp, and faba bean as single, binary, and ternary crops. A complex assessment approach (CEI value) was used to determine the impact of these crops on the agroecosystem, the interrelationships between the main indicators, and the strength of their effects. It was found that the ternary maize–hemp–faba bean crop had the most positive effect on the agroecosystem. The effectiveness of other crops was 2 to 35% less. The lowest value was calculated for the maize–faba bean crop.

Aging is one of the major etiological factors driving intervertebral disc (IVD) degeneration, the main cause of low back pain. The nucleus pulposus (NP) includes a heterogeneous cell population, which is still poorly characterized. Here, we aimed to uncover main alterations in NP cells with aging. For that, bovine coccygeal discs from young (12 months) and old (10–16 years old) animals were dissected and primary NP cells were isolated. Gene expression and proteomics of fresh NP cells were performed. NP cells were labelled with propidium iodide and analysed by flow cytometry for the expression of CD29, CD44, CD45, CD146, GD2, Tie2, CD34 and Stro‐1. Morphological cell features were also dissected by imaging flow cytometry. Elder NP cells (up‐regulated bIL‐6 and bMMP1 gene expression) presented lower percentages of CD29+, CD44+, CD45+ and Tie2+ cells compared with young NP cells (upregulated bIL‐8, bCOL2A1 and bACAN gene expression), while GD2, CD146, Stro‐1 and CD34 expression were maintained with age. NP cellulome showed an upregulation of proteins related to endoplasmic reticulum (ER) and melanosome independently of age, whereas proteins upregulated in elder NP cells were also associated with glycosylation and disulfide bonds. Flow cytometry analysis of NP cells disclosed the existence of 4 subpopulations with distinct auto‐fluorescence and size with different dynamics along aging. Regarding cell morphology, aging increases NP cell area, diameter and vesicles. These results contribute to a better understanding of NP cells aging and highlighting potential anti‐aging targets that can help to mitigate age‐related disc disease. [ABSTRACT FROM AUTHOR]

The boundary element method (BEM) is used by applying Cauchy's formula to the boundary of the water movement domain under a dam. By approximating the border with a polygon through linear interpolation, the relationships between the complex velocities on each edge of the polygon are analytically deduced. For the case of the flow domain described by a semi- circular closed contours, the numerical values of the velocity are computed and compared with those obtained only analytically. Conclusions on the analytical and numerical context are drawn. [ABSTRACT FROM AUTHOR]

The calculation of conformal mapping for irregular domains is a crucial step in deriving analytical and semi-analytical solutions for irregularly shaped tunnels in rock masses using complex theory. The optimization methods, iteration methods, and the extended Melentiev’s method have been developed and adopted to calculate the conformal mapping function in tunnel engineering. According to the strict definition and theorems of conformal mapping, it is proven that these three methods only map boundaries and do not guarantee the mapping’s conformal properties due to inherent limitations. Notably, there are other challenges in applying conformal mapping to tunnel engineering. To tackle these issues, a practical procedure is proposed for the conformal mapping of common tunnels in rock masses. The procedure is based on the extended SC transformation formulas and corresponding numerical methods. The discretization codes for polygonal, multi-arc, smooth curve, and mixed boundaries are programmed and embedded into the procedure, catering to both simply and multiply connected domains. Six cases of conformal mapping for typical tunnel cross sections, including rectangular tunnels, multi-arc tunnels, horseshoe-shaped tunnels, and symmetric and asymmetric multiple tunnels at depth, are performed and illustrated. Furthermore, this article also illustrates the use of the conformal mapping method for shallow tunnels, which aligns with the symmetry principle of conformal mapping. Finally, the discussion highlights the use of an explicit power function as an approximation method for symmetric tunnels, outlining its key points.

Artificial intelligence technologies are actively used to solve both general and highly specialized tasks. In the process of assessing (identifying) the condition of complex and heterogeneous objects, there is a high degree of a priori uncertainty regarding their condition and a small amount of initial data describing them. The trends of armed conflicts of the last decades and the regularities of the development of information systems, convincingly indicate the need to change approaches to the collection of information from various sources and their analysis. There is a constant transformation of the forms of information presentation and the order of storage and access to various types of data. The problem of integrating disparate sources of information collection into a single information space is also not fully resolved. That is why the issue of improving the efficiency of assessing the state of complex and heterogeneous dynamic objects is an important and urgent issue. The objects of research are heterogeneous dynamic objects. The subject of the research is the identification of the state of heterogeneous dynamic objects. In the research, the method of identifying the state of heterogeneous dynamic objects was developed. The novelty of the proposed method consists in: – taking into account the degree of uncertainty about the state of a heterogeneous dynamic object; – taking into account the degree of data noise as a result of distortion of data characterizing the state of a heterogeneous dynamic object; – reducing computing costs while assessing the state of heterogeneous dynamic objects; – the possibility of performing calculations with source data that are different in nature and units of measurement. It is advisable to implement the mentioned method in specialized software, which is used to analyze the state of complex technical systems and make decisions. [ABSTRACT FROM AUTHOR]

We develop new techniques involving group symmetries and complex analysis to obtain exact solutions for the transition probabilities of the M/M/1/k queueing process. These methods are based on the underlying Markovian structure of these random processes and do not involve any generating functions, Laplace transforms, or advanced special functions. Our techniques exploit the intrinsic group symmetries for both the state spaces and the matrix generators of the Markov processes related to the M/M/1/k queue. These results complement and extend the previous transient solutions given by Takács (Introduction to the theory of queues. University texts in the mathematical sciences, Oxford University Press, New York, 1962). Much of the inspiration for this work comes from viewing this queueing process as a fundamental Markovian model for the dynamics of a bike sharing station. The exact transient analysis for a related stopped version of this process can be used to address fundamental decision-making issues for managing bike-sharing services. [ABSTRACT FROM AUTHOR]

We formulate and prove Cutkosky’s Theorem regarding the discontinuity of Feynman integrals in the massive one-loop case up to the involved intersection index. This is done by applying the techniques to treat singular integrals developed in Fotiadi et al. (Topology 4(2):159–191, 1965). We write one-loop integrals as an integral of a holomorphic family of holomorphic forms over a compact cycle. Then, we determine at which points simple pinches occur and explicitly compute a representative of the corresponding vanishing sphere. This also yields an algorithm to compute the Landau surface of a one-loop graph without explicitly solving the Landau equations. We also discuss the bubble, triangle and box graph in detail. [ABSTRACT FROM AUTHOR]

Industrial wastewater, domestic wastewater, and stormwater are the three entry points for microplastics (MP) in wastewater treatment plants. Extreme weather conditions, such as rising temperatures and heavy rainfall caused by climate change, can alter the rate at which MP enters wastewater treatment plants. In this study, wastewater and sludge samples from different treatment stages were collected during a 12-month sampling campaign (seasonal) to determine the efficiency of a municipal wastewater treatment plant in removing microplastic particles. MP ranging from 20 to 1000 µm were detected and classified by shape, color, size, and chemical composition. All samples contained MP particles, with concentration ranging from 1964 ± 50–2982 ± 54 MP/L in influent to 744 ± 13–1244 ± 21 MP/L in effluent and 91.1 ± 8–61.9 ± 5 MP/g in sludge; 71.6–90.1% identified particles were fragment-type with black, white, and transparent colors. Most of the microplastic particles were removed in the activated sludge tank, while the average removal rate in the wastewater treatment plant was 57%. The total concentration of MP was 27% higher in spring than in other seasons. The most common microplastic particles were polyethylene terephthalate (PET), polystyrene (PS), and polypropylene (PP). These results demonstrate the value of long-term monitoring and MP quantification, which would provide a more accurate estimate of MP pollution from wastewater treatment plants. [ABSTRACT FROM AUTHOR]

Trace reconstruction considers the task of recovering an unknown string $\mathbf {x}\in \{0,1\}^{n}$ given a number of independent “traces”, i.e., subsequences of $\mathbf {x}$ obtained by randomly and independently deleting every symbol of $\mathbf {x}$ with some probability $p$. The information-theoretic limit of the number of traces needed to recover a string of length $n$ is still unknown. This limit is essentially the same as the number of traces needed to determine, given strings $\mathbf {x}$ and $\mathbf {y}$ and traces of one of them, which string is the source. The most-studied class of algorithms for the worst-case version of the problem are “mean-based” algorithms. These are a restricted class of distinguishers that only use the mean value of each coordinate on the given samples. In this work we study limitations of mean-based algorithms on strings at small Hamming or edit distance. We show that, on the one hand, distinguishing strings that are nearby in Hamming distance is “easy” for such distinguishers. On the other hand, we show that distinguishing strings that are nearby in edit distance is “hard” for mean-based algorithms. Along the way, we also describe a connection to the famous Prouhet-Tarry-Escott (PTE) problem, which shows a barrier to finding explicit hard-to-distinguish strings: namely such strings would imply explicit short solutions to the PTE problem, a well-known difficult problem in number theory. Furthermore, we show that the converse is also true, thus, finding explicit solutions to the PTE problem is equivalent to the problem of finding explicit strings that are hard-to-distinguish by mean-based algorithms. Our techniques rely on complex analysis arguments that involve careful trigonometric estimates, and algebraic techniques that include applications of Descartes’ rule of signs for polynomials over the reals. [ABSTRACT FROM AUTHOR]

The effective resistivity and the effective Hall parameter for two-periodic rectangular and regular triangular two-phase heterogeneous structures are analytically evaluated. In particular, it is proved that both of these parameters for a square and triangular checkerboard are the same and do not depend on the power and direction of the external imposed field. In the case of rectangular (non-square) structure, both effective parameters depend significantly on the direction of the external field, but not on its power. The extreme properties of the obtained parameters are studied. [ABSTRACT FROM AUTHOR]

The boundary element method (BEM) is used by applying Cauchy’s formula to the boundary of the water movement domain under a dam. By approximating the border with a polygon through linear interpolation, the relationships between the complex velocities on each edge of the polygon are analytically deduced. For the case of the flow domain described by a semi- circular closed contours, the numerical values of the velocity are computed and compared with those obtained only analytically. Conclusions on the analytical and numerical context are drawn.

We review the main contributions of Professor Gabriela Kohr in her studies in the Geometric function theory in several complex variables and complex Banach spaces with special emphasis on the theory of Loewner chains and the Loewner differential equation. [ABSTRACT FROM AUTHOR]

The symmetric dielectric slab waveguide serves as an important canonical structure for the high-speed high-bandwidth optical and opto-electronic silicon-on-insulator interconnects. A stochastic model of propagation loss, due to electromagnetic wave scattering with surface-roughness of the nano-scale waveguide excited at frequencies in the 100s of THz, provides useful insights for analysis and design optimization of optical interconnects. In this work, we propose an analytic solution for the stochastic scattering integral based on contour integration of the exponential autocorrelation function in the complex s-plane that improves performance at larger autocorrelation length values, compared to previous works. An expression is proposed for computing the upper-bound value of scattering loss. Results show that the proposed 2D formulation offers reasonable correlation against data from experimental measurements of loss by previous investigators, while several discrepancies are noted compared to previous 2D models. An expression is proposed for the transverse magnetic (TM) modal field amplitude, and several discrepancies in the transverse electric (TE) modal amplitudes are noted compared to previous works. A method is proposed for computation of the effective index (and propagation constant) for arbitrary cladding that improves convergence of the Newton search method, and it is compared to two other methods. Background discussions include the stochastic theory and assumptions that lead to the stationary and ergodic treatment of the surface-roughness, extension of the ensemble-average and time-average to the spatial domain, and effective thickness due to the Goos-Hänchen shift.

We give a framework to study the connectedness of the set of zeros of power series with coefficients in a finite subset G ⊂ C. We prove that the set of zeros in the unit disk is connected and locally connected if some graph on the set G of coefficients is connected. Furthermore, we apply this result to the study of the Mandelbrot set M n for fractal n -gons. We prove that M n is connected and locally connected for any n. [ABSTRACT FROM AUTHOR]

• Theoretical model is to estimate wrinkling capability of membrane with holes. • Wrinkle-free membrane with optimized irregular holes is achieved by PSO algorithm. • An empirical wrinkle-free approach is proposed without excessive optimization. Membranes are easy to buckle and wrinkle due to their extreme flexibilities, leading to the performance degradation and hampering the engineering applications. Here we propose a wrinkle-free approach through optimizing the shape and distribution of interior irregular holes in the membrane. A theoretical model with Marguerre function and complex analysis is performed to accurately estimate the stress distribution and wrinkling capability of the non-uniform membrane. The non-gradient particle swarm optimization (PSO) algorithm is implemented to determine the optimized holes to achieve wrinkle-free performance with ignorable area loss, the computational efficiency has been significantly enhanced through the superposition method. Both post-buckling analyses and physical experiments are carried out to verify wrinkle-free performance of membranes with optimized holes. In addition, an easy-to-implement empirical method is provided to guide the design of wrinkle-free membranes with arbitrary aspect ratio. [Display omitted] [ABSTRACT FROM AUTHOR]

We deduce a number of new estimates for the proximity of a binomial distribution to the corresponding Poisson distribution in the uniform metric and propose a combined approach to estimate this uniform distance when, for small and large , the estimation is performed by computer calculating and the estimates obtained in the paper are used for the remaining values of and . [ABSTRACT FROM AUTHOR]

In a recent article, Crider recommends ending a course with a memorable learning experience, called an epic finale, instead of a final exam. Here, we give the details of epic finales given in four mathematics courses: Discrete Mathematics, Information and Coding Theory, Real Analysis, and Complex Analysis. We describe how to reconfigure a course to allow for this type of closing activity and give suggestions for how to create an epic finale. [ABSTRACT FROM AUTHOR]

The article is devoted to the study of the role of diagnosis in making informed management decisions to increase the stability and efficiency of the business entity. Diagnosis is the process of assessing the condition of an object, subject, phenomenon, or management process. Diagnosis allows you to identify "bottlenecks" and weaknesses. Diagnosis includes the process of recognizing and identifying negative (crisis) situations and phenomena in business on the basis of certain dependencies, local changes in the current activities of the enterprise. Diagnosis is not a one-time procedure and requires systematic implementation. The effectiveness of the diagnosis is determined by experience. The use of complex analysis diagnostics of the enterprise allows to assess the impact of external and internal environment on the results of financial activities of the enterprise. This diagnosis is based on the use of the R-analysis method and the DuPont method. With the help of R-analysis it is possible to estimate the change of financial indicators in dynamics; perform express-diagnostics and complex diagnostics. At the same time, the weak points of the enterprise's activity are recognized in advance and the necessary measures are taken to eliminate them. DuPont diagnosis allows to ensure the harmonization of sources of formation of stocks and costs for making sound strategic and tactical management decisions. Also, this diagnostic allows you to take into account the financial situation in the market of the enterprise. DuPont diagnosis allows to ensure the harmonization of sources of formation of stocks and costs for making strategic and tactical management decisions. Also, this diagnostic allows you to take into account the financial situation in the market of the enterprise. The results of a complex analysis are used to develop a business development strategy. A complex analysis should be performed on a regular basis, as it is important for establishing financial status. Diagnosis is a process of studying the economic condition of the enterprise on the basis of analysis and synthesis of information. This process is aimed at timely anticipation of the shortcomings of entrepreneurial activity, identification of development reserves with their subsequent use. Also, the diagnostic process includes ensuring optimal management decisions.

We introduce a new approach to (deterministic) integer factorisation, which could be described in the cryptographically fashionable term of “factoring with hints”: we prove that, for any ϵ > 0, given the knowledge of the factorisations of O(N1/3+ϵ) terms surrounding N = pq product of two large primes, we can recover deterministically p and q in O(N1/3+ϵ) bit operations. This shows that the factorisations of close integers are non trivially related and that consequently one can expect more results along this line of thought.

The alignment of spindle-shaped cells in two-dimensional geometries induces singular points called topological defects, at which the alignment angle of the cell cannot be defined. To control defects related to biological roles such as cell apoptosis, calculation methods for predicting the defect positions are required. This study proposes an explicit calculation method for predicting cell alignment and defect positions in non-circular geometries. First, a complex potential is introduced to describe the alignment angles of cells, which is used to derive an explicit formula for cell alignment in a unit disc. Then, the derived formula for the unit disc is extended to the case for non-circular geometries using a numerical conformal mapping. Finally, the complex potential allows a calculation of the Frank elastic energy, which can be minimized with respect to the defect positions to predict their equilibrium state in the geometry. The proposed calculation method is used to demonstrate a numerical prediction of multiple defects in circular and non-circular geometries, which are consistent with previous experimental results.

Modern conditions of entrepreneurial activity require business entities to be competitive, to implement the achievements of science and technology, to increase the efficiency of their activities. Today, most domestic and foreign scientists interpret the efficiency of economic activity of the enterprise as a complex category that reflects the ratio of the result to the costs incurred. Since the results of economic activity can be evaluated in kind, social, value, to study the effectiveness of economic activity, it is reasonable to apply the comprehensive approach, which involves considering the object of study from the standpoint of integrity and system. Thus, the comprehensive study of business efficiency is an important component of the enterprise management system. The article scientifically substantiates and proves the need for the comprehensive study of the efficiency of economic activity of the enterprise, which provides a systematic approach to the analysis of performance, development of measures to improve the financial condition of the business entity, improving the strategy of further development. The methods of analysis of economic activity of the enterprise are considered and generalized. The indicators for conducting the comprehensive study of the efficiency of economic activity of the enterprise are determined. The main factors influencing the performance indicators to improve the enterprise management system are identified. The requirements to analytical work in the process of realization of complex researches of enterprise activity are generalized.