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This paper devotes to the study of the classical Abel equation d x d t = g (t) x 3 + f (t) x 2 , where g (t) and f (t) are trigonometric polynomials of degree m ≥ 1. We are interested in the problem that whether there is a uniform upper bound for the number of limit cycles of the equation with respect to m , which is known as the famous Smale-Pugh problem. In this work we generalize an idea from the recent paper (Yu, Chen and Liu, Disc. Cont. Dyn. Syst. Ser. B, 2023) and give a new criterion to estimate the maximum multiplicity of limit cycles of the above Abel equations. By virtue of this criterion and the previous results given by Álvarez et al. and Bravo et al., we completely solve the simplest case of the Smale-Pugh problem, i.e., the case when g (t) and f (t) are linear trigonometric, and obtain that the maximum number of limit cycles, is three, which gives a positive answer to the sixth of 33 open problem proposed by Gasull in paper (Gasull, SeMA J., 2021). [ABSTRACT FROM AUTHOR]

Let X1,X2,...,XN, N ∈ N , be independent but not necessarily identically distributed discrete and integervalued random variables. Assume that X1 ⩾ m1, X2 ⩾ m2,... , XN ⩾ mN almost surely, where m1,m2,... , mN are some integer numbers such that m1 + m2 + ⋯ +mN < 0, and Xk = d Xk+N for all k ∈ N in the sequence X1,X2,.... In this paper, we make use of some known results to provide a closed-form expression of the limit distribution function P(max{X1, X1+X2,...} ⩽ x) = P(X1 ⩽ x, X1 + X2 ⩽ x,...), x ∈ Z , via (a) inclusion–exclusion principle-based sum-product of the roots of GN(s) = 1, where GN(s) is the probability generating function of SN = X1+X2+ ⋯ +XN, (b) the probability mass function of SN, and (c) the expectation ESN. [ABSTRACT FROM AUTHOR]

Kikuchi‐Fujimoto Disease (KFD), also known as Kikuchi disease or Kikuchi histiocytic necrotizing lymphadenitis, is a rare and self‐limiting condition characterized by cervical lymphadenopathy and fever, primarily affecting young Asian adults. The aetiology of KFD remains unknown, although various infectious agents have been suggested as potential triggers. With the emergence of the COVID‐19 pandemic, cases of post‐COVID‐19 KFD and post‐COVID‐19 vaccine KFD have been reported. In this article, we present the first case of post‐COVID‐19 KFD in Hong Kong. A 24‐year‐old man developed fever and painful neck swelling 1 month after recovering from COVID‐19. Diagnostic evaluation, including ultrasound‐guided fine needle aspiration cytology (FNAC), confirmed the diagnosis of KFD. The patient's symptoms resolved spontaneously with supportive care. This case underscores the importance of considering KFD as a potential differential diagnosis in patients presenting with cervical lymphadenopathy and fever following COVID‐19 recovery or vaccination. [ABSTRACT FROM AUTHOR]

This paper proposes a novel metaphor-less optimization algorithm which makes use of maximum and minimum values obtained in the current candidate group and their interaction, hence it is named as max–min-greedy-interaction (MaGI) algorithm. The algorithm begins with the candidate group initialization and identification of maximum and minimum values of candidates. These values are utilized during updation and greedy interaction among the candidates. The proposed algorithm is also applied to synthesize four-bar linkage for prescribed path. It is reported that the MaGI performs better in comparison with the contemporary and well-established algorithms. The algorithm's effectiveness and performance have been validated on three unimodal unconstrained functions (for exploitation ability), three constrained, and three non-trivial mechanism problems (for exploration ability) which makes the algorithm acceptable and reliable for varied applications. [ABSTRACT FROM AUTHOR]

The Wiener index is one of the most classic and widely used indicators in topology. It reflects the average distance of any node pair in the graph. It not only makes the boundaries of given graphs clearer but also continuously generates topological indices that are more suitable for new fields, such as the Gutman index. The Wiener index and Gutman index are two important topological indices, which are commonly used to describe the characteristics of molecular structure. They are closely related to the physical and chemical properties of molecular compounds. And they are widely used to predict the physical and chemical properties and biological activity of molecular compounds. In this paper, we study the vertex Gutman index and Gutman index and describe the structural characteristics of all cases of two simple cycles intersecting. We comprehensively analyze the Gutman index and vertex Gutman index in these cases in detail by means of classification discussion and analogical reasoning and characterize their maximum and minimum accordingly. [ABSTRACT FROM AUTHOR]

Background: Presently, there is limited guidance on the maximal dosing of psychosis drugs that is based on effectiveness rather than safety or toxicity. Current maximum dosing recommendations may far exceed the necessary degree of dopamine D2 receptor blockade required to treat psychosis. This may lead to excess harm through cognitive impairment and side effects. Aims: This analysis aimed to establish guidance for prescribers by optimally dosing drugs for psychosis based on efficacy and benefit. Methods: We used data from two dose–response meta-analyses and reviewed seven of the most prescribed drugs for psychosis in the UK. Where data were not available, we used appropriate comparison techniques based on D2 receptor occupancy to extrapolate our recommendations. Results: We found that the likely threshold dose for achieving remission of psychotic symptoms was often significantly below the currently licensed dose for these drugs. We therefore recommend that clinicians are cautious about exceeding our recommended doses. Individual factors, however, should be accounted for. We outline potentially relevant factors including age, ethnicity, sex, smoking status and pharmacogenetics. Additionally, we recommend therapeutic drug monitoring as a tool to determine individual pharmacokinetic variation. Conclusions: In summary, we propose a new set of maximum target doses for psychosis drugs based on efficacy. Further research through randomised controlled trials should be undertaken to evaluate the effect of reducing doses from current licensing maximums or from doses that are above our recommendations. However, dose reductions should be implemented in a manner that accounts for and reduces the effects of drug withdrawal. [ABSTRACT FROM AUTHOR]

We show that the expected value of the largest order statistic in Gaussian samples can be accurately approximated as (0.2069 ln (ln (n)) + 0.942) 4 , where n ∈ [ 2 , 10 8 ] is the sample size, while the standard deviation of the largest order statistic can be approximated as − 0.4205 arctan (0.5556 [ ln (ln (n)) − 0.9148 ]) + 0.5675. We also provide an approximation of the probability density function of the largest order statistic which in turn can be used to approximate its higher order moments. The proposed approximations are computationally efficient, and improve previous approximations of the mean and standard deviation given by Chen and Tyler (1999). [ABSTRACT FROM AUTHOR]

Abstract Kikuchi‐Fujimoto Disease (KFD), also known as Kikuchi disease or Kikuchi histiocytic necrotizing lymphadenitis, is a rare and self‐limiting condition characterized by cervical lymphadenopathy and fever, primarily affecting young Asian adults. The aetiology of KFD remains unknown, although various infectious agents have been suggested as potential triggers. With the emergence of the COVID‐19 pandemic, cases of post‐COVID‐19 KFD and post‐COVID‐19 vaccine KFD have been reported. In this article, we present the first case of post‐COVID‐19 KFD in Hong Kong. A 24‐year‐old man developed fever and painful neck swelling 1 month after recovering from COVID‐19. Diagnostic evaluation, including ultrasound‐guided fine needle aspiration cytology (FNAC), confirmed the diagnosis of KFD. The patient's symptoms resolved spontaneously with supportive care. This case underscores the importance of considering KFD as a potential differential diagnosis in patients presenting with cervical lymphadenopathy and fever following COVID‐19 recovery or vaccination.

The modified Z-score (mZ-score) method has been used to detect outliers in time series received signal strength (RSS) observations. Its performance is dependent on the scale estimator used, and each has advantages and disadvantages over the others. One approach to developing a scale estimator that combines the advantages of two or more scale estimators is through scale estimator hybridization. In this paper, the outlier detection performance of a mZ-score method with different hybridization approaches for Sn and median absolute deviation (MAD) scale estimators is determined and analysed. Three different hybrid scale estimators are identified, namely weighted, maximum, and average hybrid scale estimators. The performance of the mZ-score method using the three different hybrid scale estimators is determined using three experimentally generated and publicly available time-series RSS datasets. Based on the simulation results, the weighted hybrid scale estimator results in the best outlier detection performance amongst the three hybrid scale estimators. When compared to the mean-shift-based outlier detection (MOD) technique, the k-means clustering-based technique, and the density-based spatial clustering (DBSCAN) technique, the mZ-score method with the weighted hybrid scale estimator performs better with little or no false alarm and false negative detections.

Forecasting the maximum pressure exerted by cast-in-place self-compacting concrete (SCC) is a major concern for formwork designers, researchers, and site engineers to accurately design the bearing capacity of the formwork and control the casting rate for safe and fast construction. This article aims to utilize the ARX-Laguerre model, which is a data-driven model to forecast the maximum form pressure. A laboratory instrumented setup was used to cast a 2-m column using SCC made with two different types of cement. A pressure system consisting of four sensors was used to document the pressure during casting. The data were sent to the cloud at every 1-min interval for real-time monitoring. The data were used to develop the model. The results demonstrated that forecasting with the ARX-Laguerre model is highly accurate. The model can forecast the maximum pressure exerted by SCC with less complexity. The model performance was also found to be consistent with insignificant differences between actual experimental results and predicted results. With a recursive and straightforward representation, the resulting model, known as the ARX-Laguerre model, ensures the parameter number reduction. Providing fast prediction of the maximum pressure. The model enables formwork designers to forecast the form pressure to design safe formwork and also helps to control the casting rate when SCC is used.

The problem of control of the traction force direction in the course of the motion of an inertial object is considered. The maximum possible value of the traction force is constant and is determined by the maximum dry friction force. Within a finite time range, the problem of bringing an object to a given rectilinear trajectory with simultaneous velocity maximization in the appropriate direction is considered. [ABSTRACT FROM AUTHOR]

Abstract-In this article, we investigate the periodicity of a four-order maximum fuzzy difference equation with the positive fuzzy numbers for the initial values and the parameter. Firstly, we transform the maximum fuzzy difference equation into a corresponding maximum ordinary difference equations with parameters by utilizing the fuzzy set theory. Secondly, we obtain the expressions of the eventual periodic solutions for the maximum ordinary difference equations by the inequality technique, the iteration method and the mathematical induction. Finally, we achieve the expressions of the eventual periodic solutions for the maximum fuzzy difference equation. In addition, we give some numerical simulations to verify the effectiveness of our theoretical analysis. [ABSTRACT FROM AUTHOR]

General problems on maximizing the products of several positive real, rational and integer numbers whose sum is given are investigated. [ABSTRACT FROM AUTHOR]

This research analyzes the monthly drinking water consumption in the residential sector of 46 Ecuadorian towns to determine if there was greater consumption duringthe quarantine’s isolation due to COVID-19 thanthe historical values. Over 28million data were analyzed previously throughthe Box and Whisker Test, ANOVA,and Tukey to getthe average monthly consumption (CMM) and the historical maximums (CMH) for eachyear ofregistration. The standard deviation is calculated to compare the maximum consumption during quarantine (CMC) with the historical one. No town has quarantine consumption more significantthan the historical maximum, but a third of the sample reaches the historical maximum during isolation, which shouldraiseconcernsdue to recurring natural or anthropic emergencies. Consumption during the months of isolation (March, April, May,and June of 2020) hasdistinct patternsthan those of the historical ones and are attributed to migration caused by fear and unemployment caused by COVID-19, which directly affect drinking water consumption.

Influential Spanish artist Pablo Picasso utilized the concepts of minimum and maximum, and the contrast between these concepts within several aspects of the subjects he depicted. The painting of Les Demoiselles d' Avignon (1907) is analyzed as a dynamic scene of four prostitutes competing for a client, along with a madam, to construct an original Cubist geometric analysis and representation of female form that transforms naturalistic depiction. Cubism geometrically analyzes and represents anatomy utilizing the triangle, curve, cone, circle, rectangle, square, cylindrical, and trapezoid forms involving simultaneous multiple planes and various perspectives. Les Demoiselles d' Avignon is analyzed as a dynamic progression from the most naturalistic analysis and representation of female form to a Cubist content-principled conceptual representation (Erdynast & Chen, 2014). Picasso surpasses other artists by finding a minimum or a maximum beyond what other artists had achieved, e.g., an extended elbow, or a dropped arm. Using his own remarks that are rarely utilized in other analyses of his paintings, Picasso's own agency is used to account for his objectives and to deny what he did not do. Within this paper additional works of Picasso are analyzed: The Bull Series (1945-6), Woman Ironing, (1904), Bust of a Young Woman, (1937), Weeping Woman, (1937), Massacre in Korea (1954), Final Self-Portrait Facing Death, (1972). The subjects that Picasso analyzed and represented sometimes substantially differs from the titles he gave his paintings. An analysis of the Bull Series (1945-46) by Stella Adler, a renowned acting teacher and acting coach, illustrates a formal level understanding of Picasso's very complex art (Erdynast & Chen, 2014). [ABSTRACT FROM AUTHOR]

The suggested methodology for the characterization of temperature extrema presents a multistep preprocessing procedure intended to derive extrema time series of correctly identified and thermally defined daily air temperature extrema pairs. The underlying conceptual framework for this approach was developed in response to the existing gaps in the current state of daily extrema identification and the development of extrema-based synthetic air temperature time series. A code consisting of a series of algorithms was developed to establish four-parameter criteria for a more accurate representation of daily variability that allows easy replication of temperature distribution based on the correct characterization of daily temperature patterns. The first preprocessing step consists of subjecting the high-frequency temperature time series to a theoretical diurnal observing window that imposes latitudinally and seasonally crafted limits for the individual identification of daily minima and maxima. The following pre-processing step involves the supplementation of air temperature extrema with the information on the occurrence of extrema timing deemed as vital information for the reconstruction of the temperature time series. The subsequent step involves the application of an innovative temperature pattern recognition algorithm that identifies physically homogeneous air temperature populations based on the information obtained in previous steps. The last step involves the use of a metric for the assessment of extrema temperature and timing parameters’ susceptibility to climate change. The application of the presented procedure to high-frequency temperature data yields two strains of physically homogeneous extrema time series with the preserved characteristics of the overall temperature variability. In the present form, individual elements of this methodology are applicable for correcting historical sampling and air temperature averaging biases, improving the reproducibility of daily air temperature variation, and enhancing the performance of temperature index formulae based on daily temperature extrema. The objective of this analysis is the eventual implementation of the presented methodology into the practice of systematic temperature extrema identification and preprocessing of temperature time series for the configuration of physically homogeneous air temperature subpopulations.

A sufficient condition for solvability in natural numbers of linear Diophantine equation is obtained and a problem on maximizing the product of powers natural numbers whose corresponding weighted sum is given is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we consider the asymptotic behaviors of moment for normalized extreme of the generalized gamma distribution. Under optimal norming constants, we establish higher-order expansion of moment for the maximum. The expansion is used to deduce the rate of convergence of the moment for normalized partial maximum to the moment of the associating extreme value limit. Numerical simulations are given to sustain the results of our findings. [ABSTRACT FROM AUTHOR]

The Wiener index is one of the most classic and widely used indicators in topology. It reflects the average distance of any node pair in the graph. It not only makes the boundaries of given graphs clearer but also continuously generates topological indices that are more suitable for new fields, such as the Gutman index. The Wiener index and Gutman index are two important topological indices, which are commonly used to describe the characteristics of molecular structure. They are closely related to the physical and chemical properties of molecular compounds. And they are widely used to predict the physical and chemical properties and biological activity of molecular compounds. In this paper, we study the vertex Gutman index and Gutman index and describe the structural characteristics of all cases of two simple cycles intersecting. We comprehensively analyze the Gutman index and vertex Gutman index in these cases in detail by means of classification discussion and analogical reasoning and characterize their maximum and minimum accordingly.

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Definition: The suggested methodology for the characterization of temperature extrema presents a multistep preprocessing procedure intended to derive extrema time series of correctly identified and thermally defined daily air temperature extrema pairs. The underlying conceptual framework for this approach was developed in response to the existing gaps in the current state of daily extrema identification and the development of extrema-based synthetic air temperature time series. A code consisting of a series of algorithms was developed to establish four-parameter criteria for a more accurate representation of daily variability that allows easy replication of temperature distribution based on the correct characterization of daily temperature patterns. The first preprocessing step consists of subjecting the high-frequency temperature time series to a theoretical diurnal observing window that imposes latitudinally and seasonally crafted limits for the individual identification of daily minima and maxima. The following pre-processing step involves the supplementation of air temperature extrema with the information on the occurrence of extrema timing deemed as vital information for the reconstruction of the temperature time series. The subsequent step involves the application of an innovative temperature pattern recognition algorithm that identifies physically homogeneous air temperature populations based on the information obtained in previous steps. The last step involves the use of a metric for the assessment of extrema temperature and timing parameters' susceptibility to climate change. The application of the presented procedure to high-frequency temperature data yields two strains of physically homogeneous extrema time series with the preserved characteristics of the overall temperature variability. In the present form, individual elements of this methodology are applicable for correcting historical sampling and air temperature averaging biases, improving the reproducibility of daily air temperature variation, and enhancing the performance of temperature index formulae based on daily temperature extrema. The objective of this analysis is the eventual implementation of the presented methodology into the practice of systematic temperature extrema identification and preprocessing of temperature time series for the configuration of physically homogeneous air temperature subpopulations. [ABSTRACT FROM AUTHOR]

Air temperature is a measure of temperature at different levels of the Earth's atmosphere. It is governed by many factors, including incoming solar radiation, humidity and altitude. When discussing surface air temperature, the annual atmospheric temperature range at any geographical location depends largely upon the type of biome, as measured by the Köppen climate classification. Air temperature describes the process of measuring a current local temperature for immediate or later evaluation. Datasets consisting of repeated standardized measurements can be used to assess temperature trends. Temperature varies greatly at different heights relative to Earth's surface and this variation in temperature characterizes the four layers that exist in the atmosphere. These layers include the troposphere, stratosphere, mesosphere, and thermosphere. The aim of this paper was to analyze air temperature in the Republic of North Macedonia over the span of 10 years, measured in 26 different cities. Considering the fact that North Macedonia has a decent geographical position and also the relief, the extent and direction of the mountain slopes and their height are important climatic factors which also effect on the air temperature of our country. [ABSTRACT FROM AUTHOR]

In this work, we present a new class of continuous distributions called the exponentiated reduced-Kies-G family. The basic mathematical properties of the new family are addressed. A special sub-model of the proposed family, called the exponentiated reduced-Kies exponential (ERKiEx), is studied in detail concerning the aspect of estimation and inference, we described eight estimation methods. A comprehensive set of simulation studies are performed to compare and rank the proposed methods based on partial and overall ranks. Two real-life reliability engineering data applications are employed to explore the applicability and flexibility of the new ERKiEx distribution as compared to well-known other exponential extensions such as the Marshall{Olkin exponential, Kumaraswamy exponential and exponentiated exponential distributions. [ABSTRACT FROM AUTHOR]

A novel multi band frequency reconfigurable MIMO antenna with Ultra-wide band sensing is designed, fabricated, tested and compared the simulation and measured results. The antenna structure contains two planar inverted F shape antennas with Meandered line structures to provide a frequency reconfigurability for communication and U-shape UWB sensing antenna was integrated with MIMO Meandered line elements for spectrum sensing. PIN diodes are used for on/off switch to attain a frequency reconfigurability and provides a communication in different modes. Varactor diodes are used for tuning over the wide band. The proposed sensing antenna is used to cover a wide frequency band from 0.3GHz-3GHz and provides a frequency reconfigurability over the three bands based on PIN diode switching (0.7GHz-0.85GHz, 1.25GHz-1.45GHz, 1.6GHz-3GHz). The antenna system developed on a single FR4 substrate area of 120mmx65mmx1.4mm in size. The proposed method used to achieve frequency reconfigurable ultra-wide band MIMO provides high gain of 4dB at single frequency and more than 2dB at multi-band frequencies with better efficiency. Therefore, the proposed antenna design provides a multi-band operation in UWB range with minimal size. Same Antenna is used for sensing and Communication & UWB antenna in MIMO Configuration, The MIMO AND UWB sensing antenna exhibit stable gain, good efficiency and provides omnidirectional radiation pattern over the desired bands. [ABSTRACT FROM AUTHOR]

An important topic in the field of geometric optimization is finding the largest rectangle separating two different points sets, which has significant applications in circuit design and data science. We consider some extensions of the maximum bichromatic separating rectangle (MBSR) problem. In one of the extensions, the optimal rectangle may include up to k outliers, where k is given as part of the input. This extension and is called MBSR with outliers or MBSR-O. In this paper, we improve the current known time bounds for MBSR-O from O (k 7 m   log m + n) to O (k 3 m + k m   log m + n) using a clever staircase sweep approach. We also propose another extension, which is named MBSR among circles or MBSR-C and asks for the largest rectangle separating red points from blue unit circles. Our solution to MBSR-C is an O (m 2 + n) -time algorithm that involves an optimized scanning of all candidate circle arcs for locations of potential optimal solutions. [ABSTRACT FROM AUTHOR]

Scalar limit operators (or superlative scalar modifiers), such as at least and at most , have been shown to develop a range of functions crosslinguistically. This article brings to the discussion evidence from Russian – operators based on the construction po + Adj + mere 'by + Adj + measure' – and interprets synchronic patterns of associated functions in light of historical change. The construction has given rise to several lexicalized operators, both minimal and maximal, which, similarly to their counterparts in other languages, evoke different kinds of scales pertaining to representational, evaluative, or illocutionary (rhetorical) domains. A corpus-based analysis of their usage across three centuries has revealed a narrowing down of lexical variation within the construction, attributable to competition of different variants for the speaker's selection, and a reduction of the functional overlap between the variants. The data also suggest reorganization of the functional repertoire within particular variants. For the most frequent operator, po krajnej mere 'at least' lit. 'by the extreme measure', the share of 'rhetorical' observations has increased over the years while that of 'evaluative' ones has shrunk. • The article explores Russian [po + Adj + mere]-based scalar limit operators. • They evoke various scales in representational, evaluative or illocutionary domains. • Lexical variation within the construction has substantially decreased. • Functional overlap has also shrunk. • The reason for uneven distribution of uses between the variants is not semantic. [ABSTRACT FROM AUTHOR]

The article focuses on the application of mathematical methods in economics, in particular discussing economic problems that are easily solved using derivatives. The purpose of the article is to show students the way and opportunity to use mathematical methods to solve economic problems. To this end, the article discusses and analyzes several economic tasks in detail, which will be interesting and easy for students to master. I considered the derivative of a function as the rate of change and introduced the definition: The instantaneous rate of change of the function f with respect to x at a point is called the derivative if it exists. With the help of this definition I have discussed and explained Task 1: Suppose that the increase in production of a certain product over a period of time is described by a function And population growth is described by the following function: Where is the number of years from the initial period, then the production of these products per capita is given by the function: Find the growth rate of product production. By solving this task I came to the conclusion that after a year the production of products per capita increases. In the following tasks I used the method of finding the extremum values of a function using a derivative, namely I equated the first-order derivative to 0, found the critical points, and with the help of the second-order derivative I determined the extremes of the function. I discussed task 2: For the production of X volume of products, the firm plans a cost that is calculated by the formulan . For what volume of production will the average cost be the smallest? Find the numerical value of this small expense. Solving this problem, I came to the conclusion that the given function of the average cost takes on the least value when the output volume is a unit , and this value is equal to: which is the marginal cost when producing the volume output. I discussed Task 3: How many products should be sold in order for a firm to profit maximally if the derivative cost function is known: And return function: Here I came to the conclusion: if 600 units of the product are sold, then the firm's profit will be maximum and it will be numerically equal At the end of the article I discussed such a task 4 of applied optimization. What is the minimum amount of material needed to make a 2 liter cylindrical jar? Where I came to the conclusion: the smallest amount of material will be spent to get a cylindrical vessel if we take the height 2 times the radius of the base.

Copyright of Adab Al-Kufa is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study analyzed the determinants of household demand for food away from home (FAFH) in Riyadh, Saudi Arabia. Truncated generalized Poisson regression (TGPR) and truncated standard Poisson regression (TSPR) was applied to data from a random sample of 101 families. Maximum likelihood was used to obtain parameter estimates for these two models. TGPR was found to be optimal and appropriate for the analysis of demand data. Both income and number of household members had a significant positive effect, which is consistent with economic logic and reality in Saudi society. Price and taste also had positive effects on FAFH demand. Household income as an economic variable has a significant positive effect on the number of times that a household dines out during the month. When income increases by one thousand Saudi riyals, the demand will increase by 11%, which is consistent with economic logic. Household income as a quantitative economic variable and the number of household members as a quantitative demographic variable are the most important variables in household demand for FAFH. However, the effect of income is more significant than that of the number of household members. As this study investigated the impact of socio-economic and demographic factors on food away from home (FAFH) demand in Riyadh such as household income, number of household members, education level, prices and cleanness of restaurant, and taste of food. Still there are other variables could be used as potential variables could affect FAFH demand in Saudi Arabia in future research such as the change in number of working women which there is shift in the number of female workers recently. The future studies could look at the differences in socio-economic between consumers for different types of restaurants such as traditional, fast food, fish, and luxury restaurants. Due to the high demand for restaurant meals, officials should tighten the health control and close restaurants that do not comply with health requirements as well security and safety requirements. Restaurants should pay attention to improving the quality of meals and offering them at affordable prices to consumers.

Jacobi’s zeta function has appeared in problems of science and engineering. Thus, its extrema are helpful for solving the related problems. For example, Bowman (Proc Lond Math Soc s2–39:205–215, 1935) used the maximum to calculate the capacity of two-dimensional ordinary condensers when the modulus is very close to one due to practical interest. Since the maximum tends to one in this case, this paper examines the speed of convergence by comparing the maximum minus one with some other functions which converge to zero. Lastly, this paper presents a formula expressed in terms of elementary functions to describe the maximum asymptotically as the reciprocal of the complementary modulus approaches infinity. [ABSTRACT FROM AUTHOR]

On April 17, 2020, one male specimen of the shi drum, Umbrina cirrosa (Linnaeus, 1758) was measured as 104 cm in total length, weighed 11080 g, and 18 years old. The U. cirrosa were sampled at 2 m depth by using trammel net in Ordu at the southern Black Sea. Up to date, this length, weight and age are a new record for the maximum size of U. cirrosa. These measurements make it the largest individual in the world. [ABSTRACT FROM AUTHOR]

In this paper we investigate combinatorial constructions for w‐cyclic holey group divisible packings with block size three (3‐HGDPs). For any positive integers u,v,w with u≡0,1 (mod3), the exact number of base blocks of a maximum w‐cyclic 3‐HGDP of type (u,wv) is determined. This result is used to determine the exact number of codewords in a maximum three‐dimensional (u×v×w,3,1) optical orthogonal code with at most one optical pulse per spatial plane and per wavelength plane. [ABSTRACT FROM AUTHOR]

Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, but the maxima and minima for each Bessel function, used to match Neumann boundary conditions, have not had the same treatment. Here we compute 10000 extrema for the first 600 orders of the Bessel function J. To do this, we employ an adaptive root solver bounded by the roots of the Bessel function and solve to an accuracy of 10−19. We compare with the existing literature (to 30 orders and 5 maxima and minima) and the results match exactly. It is hoped that these data provide values needed for orthogonal function expansions and numerical expressions including the calculation of geometric correction factors in the measurement of resistivity of materials, as is done in the original paper using these data.