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In this note we offer some criticism on the paper “On an identity for zeros of Bessel functions” by Baricz et al. [3] . The paper gives identities of type Stieltjes–Calogero for the sums of reciprocals of differences of fourth powers of zeros of Bessel functions. Although interesting in principle, by containing one too many sums of similar complexity the identities fail to convey the true spirit of the work of Stieltjes and Calogero. We rectify this by providing what we think is the correct type of identity for the above-said sums, in the general setup of entire functions of order

Recently, metapopulation models for rock-paper-scissors games have been presented. Each subpopulation is represented by a node on a graph. An individual is either rock (R), scissors (S) or paper (P); it randomly migrates among subpopulations. In the present paper, we assume victory rates differ in different subpopulations. To investigate the dynamic state of each subpopulation (node), we numerically obtain the solutions of reaction-diffusion equations on the graphs with two and three nodes. In the case of homogeneous victory rates, we find each subpopulation has a periodic solution with neutral stability. However, when victory rates between subpopulations are heterogeneous, the solution approaches stable focuses. The heterogeneity of victory rates promotes the coexistence of species.

We can obtain a two-fold symmetric figure by folding a square sheet of paper in the middle and then cutting along some curves drawn on the paper. By making two perpendicular folds through the centre of the paper and then cutting, we can obtain a four-fold symmetric figure. We can also get an eight-fold symmetric figure by making a fold bisecting an angle made by the two perpendicular folds before cutting. But it is not possible to obtain a three-fold, five-fold or six-fold symmetric figure in this way; we need to make more folds before cutting. Making a three-fold (respectively five-fold and six-fold) figure involves the division of the angle at the centre (360°) of a square sheet of a paper into six (respectively ten and twelve) equal parts. In other words, we need to construct the angles 60°, 36° and 30°. But these angles cannot be obtained by repeated bisections of 180° by simple folding as in the making of two-fold, four-fold and eight-fold figures. In [1], we see that each of the constructions of 60° and 30° applies the fact that sin 30° = ½ and takes only a few simple folding steps. The construction of 36° is more tedious (see, for example, [2] and [3]) as sin 36° is not a simple fraction but an irrational number. In this Article, we show how to make, by paper-folding and cutting a regular pentagon, a five-pointed star and create any five-fold figure as we want. The construction obtained by dividing the angle at the centre of a square paper into ten equal parts is called a pentagon base. We gained much insight from [2] and [3] when developing the method for making the pentagon base to be presented below.

The design and testing of a novel vermicomposting system, acronymed FLUVTS ─ FLippable Units Vermireactor Train System ─ is presented. It enables rapid vermicomposting of paper waste without the need of pre-composting and requires animal manure supplementation to the extent of only 10:1 paper: manure mass ratio in contrast to reported systems which must have 50% or more of the feed mass as animal manure. Moreover, the system enables the vermicomposting to be accomplished at a high rate, achieving near-total convertion of feed to vermicast at solid retention times of just 30 days in comparison to conventional systems which take 90–120 days for the same process. Uninterrupted vermireactor operation for 6 months, during which the feed was put in and its vermicompost harvested once in 30 days, demonstrates the robustness and the consistency of the system. The suitability of the paper-waste vermicompost as an organic fertilizer was then tested in terms of it's effect on seed germination and early growth of four food plants chilly (Capsicum annuum), ladies finger, (Abelmoschus esculentus), cucumber (Cucumis sativus), and tomato (Lycopersicon esculentum). In general, the paper waste vermicompost when applied at levels

The large body of literature on the comparability of mean scores for self-report survey responses gathered using paper-and-pencil and computer data collection methodologies has yielded inconclusive results. However, no comprehensive meta-analysis has been conducted in this field, and those that are available for specific measures have typically not differentiated between studies using between-groups and within-subjects designs. Also, few individual studies, and no meta-analyses, have used correct statistical procedures to determine the equivalence of the two methodologies. Consequently, we conducted two meta-analyses assessing quantitative equivalence (i.e., mean scores), with the first consisting of 144 independent effect sizes from studies with between-groups designs and the second including 70 independent effect sizes from studies using within-subjects designs. Both meta-analyses assessing mean scores indicated equivalence across conditions, with large heterogeneity of variance in the between-groups analysis. Presence of others in both the paper-and-pencil and computer conditions accounted for a significant portion of this variance. Heterogeneity of variance was small for the within-subjects design analysis. Overall, results indicated that the mean scores for self-report surveys using paper-and-pencil and the computer are comparable, although heterogeneity differs for the study designs. Equivalence testing was demonstrated to be the recommended statistical procedure for this type of research.

Thamarai Selvi and Vaidya Nathan [2] discussed maximum distance on graphs. We made an extension of that paper [2]. We discussed about complete graph Kn, star graph Sn, the complete bipartite graph Km,n. In this paper, we studied about the cycle graph Cn (n being any interger ≥ 3) and the multi star graph Bm,n, where m, n are integers, both greater than or equal to 2.

Different types of paper and different basis weight of the same paper are selected in order to study the relationship between paper and color reproduction. Comparing with the reference data set, the influence of paper on color reproduction is analyzed from the color difference and color gamut. The results show that the colorimetric value of paper is more closer to the reference data set, the average color difference of patches is more smaller. The color reproduction ability of offset paper is weaker than that of other paper in the experiment. The color reproduction ability of different basis weight of the same paper is also slightly different. Therefore, the type and basis weight of the paper affect the color reproduction. In the process of printing proofs, it is considered that paper has a certain impact on color reproduction.

Counting the number of words of a certain length accepted by a non-deterministic finite automaton (NFA) is a fundamental problem, which has many applications in different areas such as graph databases, knowledge compilation, and information extraction. Along with this, generating such words uniformly at random is also a relevant problem, particularly in scenarios where returning varied outputs is a desirable feature. The previous problems are formalized as follows. The input of #NFA is an NFA N and a length k given in unary (that is, given as a string 0^k), and then the task is to compute the number of strings of length k accepted by N. The input of GEN-NFA is the same as #NFA, but now the task is to generate uniformly, at random, a string accepted by N of length k. It is known that #NFA is #P-complete, so an efficient algorithm to compute this function exactly is not expected to exist. However, this does not preclude the existence of an efficient approximation algorithm for it. In this talk, we will show that #NFA admits a fully polynomial-time randomized approximation scheme (FPRAS). Prior to our work, it was open whether #NFA admits an FPRAS; in fact, the best randomized approximation scheme known for #NFA ran in time n^O(log(n)). Besides, we will mention some consequences and applications of our results. In particular, from well-known results on counting and uniform generation, we obtain that GEN-NFA admits a fully polynomial-time almost uniform generator. Moreover, as #NFA is SpanL-complete under polynomial-time parsimonious reductions, we obtain that every function in the complexity class SpanL admits an FPRAS.

A fundamental result in statistical learning theory is the equivalence of PAC learnability of a class with the finiteness of its Vapnik-Chervonenkis dimension. However, this clean result applies only to binary classification problems. In search for a similar combinatorial characterization of learnability in a more general setting, we discovered a surprising independence of set theory for some basic general notion of learnability. Consider the following statistical estimation problem: given a family F of real valued random variables over some domain X and an i.i.d. sample drawn from an unknown distribution P over X, find f in F such that its expectation w.r.t. P is close to the supremum expectation over all members of F. This Expectation Maximization (EMX) problem captures many well studied learning problems. Surprisingly, we show that the EMX learnability of some simple classes depends on the cardinality of the continuum and is therefore independent of the set theory ZFC axioms. Our results imply that that there exist no "finitary" combinatorial parameter that characterizes EMX learnability in a way similar to the VC-dimension characterization of binary classification learnability.

The problem of chasing convex functions is easy to state: faced with a sequence of convex functions f t over d-dimensional Euclidean spaces, the goal of the algorithm is to output a point x t at each time, so that the sum of the function costs f t (x t ), plus the movement costs ||x t − x t − 1 || is minimized. This problem generalizes questions in online algorithms such as caching and the k-server problem. In 1994, Friedman and Linial posed the question of getting an algorithm with a competitive ratio that depends only on the dimension d. In this talk we give an O (d)-competitive algorithm, based on the notion of the Steiner point of a convex body.

We introduce our efforts within the project ‘The science of deep specification’ to work out the key formal underpinnings of industrial-scale formal specifications of software and hardware components, anticipating a world where large verified systems are routinely built out of smaller verified components that are also used by many other projects. We identify an important class of specification that has already been used in a few experiments that connect strong component-correctness theorems across the work of different teams. To help popularize the unique advantages of that style, we dub itdeep specification, and we say that it encompasses specifications that arerich,two-sided,formalandlive(terms that we define in the article). Our core team is developing a proof-of-concept system (based on the Coq proof assistant) whose specification and verification work is divided across largely decoupled subteams at our four institutions, encompassing hardware microarchitecture, compilers, operating systems and applications, along with cross-cutting principles and tools for effective specification. We also aim to catalyse interest in the approach, not just by basic researchers but also by users in industry.This article is part of the themed issue ‘Verified trustworthy software systems’.

There is no simple definition of the slope for multicomponent systems because the vapour liquid equilibrium is represented by a surface (which lies in hyperspace for more than 3 compounds). Thus, for multicomponent systems any pseudo-binary method for estimating tray efficiencies and HETP must rely, in part, on an approximate method of estimating the slope. The objective of this paper is to present a new method of approximating the slope in multicomponent systems based on differentiation of the phase equilibrium surface with respect to the mole fraction of the design component, defined as that compound we seek to eliminate from the mixture in a particular section of the column. There is only one design compound per column section. The approach presented here can be easily applied to absorber and stripper columns, where the concept of key components is not applicable. Two analytical approximate methods of estimating the design slope are shown to be in good agreement with the rigorous calculation even in cases where the relative volatility is not constant. These simple approximations, which need nothing beyond what is readily available from any column simulation program are adequate for design and can be programmed easily in any spreadsheet.

In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.

The analysis of dielectric response function obtained from the power transformer is a well-accepted technique in insulation diagnosis. A convenient way of analysing time-domain dielectric response φ(t) is the formulation of simple resistance−capacitance-based circuits like the conventional Debye model (CDM) or the modified Debye model (MDM) that are capable of modelling φ(t). However, available techniques do not guarantee unique branch parameters of such circuits for a given φ(t). In fact, the branch parameters are known to depend on the curve-fitting procedure opted during model formulation. This makes accuracy of CDM and MDM parameter-based diagnosis techniques less reliable. Furthermore, it seems logical to analyse the time-domain dielectric response of oil-paper insulation using a model containing time-varying parameters. In this study, a methodology is proposed using which such an insulation model (containing time-varying parameters) is formulated using time-domain insulation response. Related analysis presented suggests that the proposed model is immune to problems associated with available insulation models (containing time-invariant parameters). The performance of the proposed model in indicating insulation condition is tested on data obtained from several real-life power transformers.

This paper provides results of the investigation of arrays of Russian publications in 252 specified thematic areas for 2010–2017 according to the Web of Science Core Collection (WoS CC). This period is characterized by an increase in the Russian document flow. In 87 scientific areas, Russia reached the level of the top 10 countries for the number of publications submitted to WoS CC. However, in most scientific areas, the citation of Russian publications lags far behind the global average. The average level of citation for the study period matched or exceeded the global average only in 15 areas. The most successful research area for Russia, both in terms of the share component in the number of publications in the world and in the level of their citation, is Nuclear Physics. Other successful areas are those for which Russia reached the top 3% of countries regarding the number of publications: Spectroscopy; Mathematics; Physics, Mathematical; Chemistry, Inorganic & Nuclear; Geochemistry & Geophysics; Mining & Mineral Processing; and Engineering, Petroleum.

This paper aims at presenting pairs of rectangles representing the same sphenic number where, in each pair, the sum of the areas is 2 times sphenic number -1

Sunaga considered all computational procedures, which had beenВ traditionally defined on real numbers, as being too ideal andВ proposed to replace them by the procedures on real intervals inВ order to make everything "more realistic". Sunaga studied manyВ different kinds of numerical procedures including the Taylor-seriesВ interval solution of the initial-value problem of ordinaryВ differential equations.The purpose of the present note is to mark the 60-th anniversary of the publication of the seminal work by the Japan mathematician Teruo Sunaga. The paper summarizes the results of his Master Thesis. Sunaga's work sets the foundation of the contemporary interval analysis and reliable computing. This is an interdisciplinary field, combining abstract mathematical theories and practical applications related to computer science, numerical analysis and mathematical modeling in the natural, engineering and social-economic sciences.

Migration paths of animals are rarely the same. The paths may change according to seasonal and circadian rhythms. We study the effect of temporal migration on population dynamics of rock-paper-scissors (RPS) games with mutation by using the metapopulation dynamic model with two patches. Via mutation, an individual R changes to S with rate μ. All agents move by random walk between two patches and the RPS game is performed in each patch. The migration path between two patches is switched on or off periodically. The dynamics are represented by the reaction-diffusion equations with time-dependent diffusion coefficients in diffusively coupled reactors. We obtain the solutions of time-dependent reaction-diffusion equations numerically and analytically. The time-varying migration path induces complex behavior for the RPS dynamics, depending on the frequency of the periodical path. We find that the phase transitions occur by varying mutation rate μ. The phase transition depends highly on the frequency.

We give an overview of our critiques of "proofs" of security and a guide to our papers on the subject that have appeared over the past decade and a half. We also provide numerous additional examples and a few updates and errata.

In this paper, we consider precoder designs for multiuser multiple-input-single-output (MISO) broadcasting channels. Instead of using a traditional linear zero-forcing (ZF) precoder, we propose a generalized ZF (GZF) precoder in conjunction with successive dirty-paper coding (DPC) for data-transmissions, namely, the GZF-DP precoder, where the suffix \lq{}DP\rq{} stands for \lq{}dirty-paper\rq{}. The GZF-DP precoder is designed to generate a band-shaped and lower-triangular effective channel $\vec{F}$ such that only the entries along the main diagonal and the $\nu$ first lower-diagonals can take non-zero values. Utilizing the successive DPC, the known non-causal inter-user interferences from the other (up to) $\nu$ users are canceled through successive encoding. We analyze optimal GZF-DP precoder designs both for sum-rate and minimum user-rate maximizations. Utilizing Lagrange multipliers, the optimal precoders for both cases are solved in closed-forms in relation to optimal power allocations. For the sum-rate maximization, the optimal power allocation can be found through water-filling, but with modified water-levels depending on the parameter $\nu$. While for the minimum user-rate maximization that measures the quality of the service (QoS), the optimal power allocation is directly solved in closed-form which also depends on $\nu$. Moreover, we propose two low-complexity user-ordering algorithms for the GZF-DP precoder designs for both maximizations, respectively. We show through numerical results that, the proposed GZF-DP precoder with a small $\nu$ ($\leq\!3$) renders significant rate increments compared to the previous precoder designs such as the linear ZF and user-grouping based DPC (UG-DP) precoders., Comment: 31 pages, 13 figures, submitted to IEEE Transactions on Wireless Communications in Aug. 2016

Bu çalışmanın amacı, GeoGebra ve Kağıt-Kalem gruplarında geometri soruları çözen ortaokul matematik öğretmen adaylarının argümantasyon yapılarının doğasını incelemektir. Bu çalışmada nitel durum çalışması deseni kullanılmış ve veriler 2013-2014 akademik yılının sonbahar döneminde 16 ortaokul matematik öğretmen adayından toplanmıştır. Veri kaynaklarını uygulamaların video kayıtları, odak grup görüşmeleri ve belgeler oluşturmaktadır.Bulgularda beş çeşit global argümantasyon yapısı ortaya çıkmıştır. Bunların ikisi Çizgi/Hat yapı ve Bağımsız-Argümanlar yapısı bu çalışmada ortaya çıkmıştır. Ayrıca katılımcılar 9 çeşit lokal argüman yapılarından üçünü çok sık kullanmayı tercih etmişlerdir. Son olarak, katılımcıların gerekçelendirmelerine odaklanarak lokal argümantasyonları incelenmiştir. Bu analiz, ortaokul matematik öğretmen adaylarının GeoGebra ve Kağıt-Kalem gruplarında geometri soruları çözerken kullandıkları lokal argümantasyonların niteliğini ortaya çıkarmıştır. The purpose of the current study was to investigate the nature of argumentation structures of prospective middle school mathematics teachers while solving geometry tasks within the GeoGebra and Paper-Pencil groups. The study employed qualitative case study design and the data of which were collected from 16 prospective middle school mathematics teachers during the fall semester of the 2013-2014 academic year. Data were based on the video recordings of the implementations, the focus group interviews and documents.The findings revealed five types of global argumentation structures, two of which emerged from the present study: Line-structure and Independent-Arguments structure. In addition, the participants employed 9 types of local arguments while three of them were most frequently preferred. Finally, the local argumentations were examined by focusing on the justifications of the participants. This analysis revealed the characteristics of the local argumentations that prospective middle school mathematics teachers use while solving geometry tasks in GeoGebra and Paper-Pencil groups. 318

In this study, we investigate a discrete-time version of logit dynamics, as applied to the rock–paper–scissors (RPS) game. First, we show that around the Nash equilibrium point, an attracting closed invariant curve appears due to the Neimark–Sacker bifurcation. Next, near the resonance point, we find a period-three attracting cycle, which can be thought of as a counterpart to the cyclically stable set in the RPS game with best response dynamics. Moreover, we show that the cycle can coexist with an attracting closed invariant curve, a period-three saddle cycle, and the attracting or repelling Nash equilibrium point. Finally, we use the codimension-two bifurcation theory to specify the set of heteroclinic bifurcations that destroy the coexistence of the attractors.

A sheet of tissue paper can change color appearance. Various colors were observed through tissues, and the appearance was quantitatively measured by the elementary color naming method. The saturation decreased with tissues, but the color appearance was fairly vivid in spite of a marked decrease of excitation purity, suggesting that visual mechanisms neglect the white color appearance to judge the color behind the tissue. A tissue was applied to the simultaneous color contrast stimulus, and a vivid color appeared on the central gray patch, which otherwise appeared just gray. The analysis of the color appearance of both the surround and the test patch suggested that the simultaneous color contrast phenomenon is a result of chromatic adaptation to the color of the surround.

In this work, a counterexample is given to refute a result in the paper by Younis et al. (J Fixed Point Theory Appl 21:1–33, 2019). Furthermore, applying this counterexample, we give negative answers to some of the open problems in their paper. Recently, Baradol et al. give a new theorem to rectify the result of Younis et al. However, we find that there are some gaps in the proofs of their results. Finally, we introduce a fundamental lemma and fill these gaps.

Oil paper insulation is the main insulation form of large transformers. Partial discharge(PD) in oil paper insulation will not only damage the insulation performance, but also is the precursor and manifestation of insulation deterioration. Weibull distribution parameter is an important characteristic parameter of PD. In this paper a method is proposed to extract the characteristic parameter of PD based on the three-parameter Weibull model, then gray wolf optimization algorithm and particle swarm optimization algorithm are used to calculate the parameters of the model. The result shows that the two algorithms can get the parameters quickly and accurately, and the model can effectively reflect the characteristics of the $H_{n}(q)$ spectrum of PD times.

Pulp and paper industries have provided great research opportunities to control systems. The objective of this study was to investigate the relationships between 80 process variables of CMP tower and stock preparation, and 17 newsprint quality properties in Mazandaran Wood and Paper Industries (MWPI). After the preparation of two suitable data series considering the time needed for pulp to paper, the relations between process dependent and newsprint independent variables were determined using partial least squares (PLS) regression. As a result, two PLS models were developed. The first model with 4 latent vectors categorized and related CMP tower variables and the second one, through 8 latent vectors connected stock preparation variables with paper properties. PLS regression coefficients determined how much the most influencing process variables impact each paper properties

To deal with the undesirable factors in Data Envelopment Analysis (DEA), a non-linear DEA model was previously developed for a paper production system, where the desirable outputs are increased and the undesirable outputs are decreased for efficiency improvement. To convert the proposed non-linear model into a linear one, a linear approximation to the non-linear constraint is used and an approximate efficiency score is obtained. In this paper, we propose a new method to solve the non-linear programming problem and calculate the efficiency scores accurately, in which a second-order cone programming (SOCP) is defined and applied to transfer the non-linear programming model into a linear one. We applied the proposed model to measure the environmental performance of 30 paper mills along the Huai River in China. It was found that the efficiency scores obtained by our model is obvious different with the ones by approximate models.