A general delta-nabla calculus of variations on time scales with application to economics

We consider a general problem of the calculus of variations on time scales with a cost functional that is the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange delta-nabla differential equations are proved, which lead to important insights in the process of discretisation. Application of the obtained results to a firm that wants to program its production and investment policies to reach a given production rate and to maximise its future market competitiveness is discussed

Necessary condition for an Euler-Lagrange equation on time scales

We prove a necessary condition for a dynamic integrodifferential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. An example of a second order dynamic equation, which is not an Euler-Lagrange equation on an arbitrary time scale, is given. © 2014 Monika Dryl and Delfim F. M. Torres

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

History as a Factor Creating the Value of a Luxury Brand

Theoretical background: The attributes of a luxury brand include both the physical characteristics of the product and the symbolic values that the brand provides to the consumers. Symbolism is interpreted as prestige, beauty, charisma, the creation of which requires larger and more time-consuming efforts than just producing a unique, expensive, high-quality product. An important aspect of a reliable, trustworthy image is the history of the brand and its creators. In the opinion of many authors, it is an important element of the brand’s value, not only shaping its luxurious image, but also providing psychological values. Although history is not always indicated directly among the attributes of luxury brands, it is the basis of other values ascribed to them. The luxurious nature of the brand is often defined in the literature through the prism of its symbolism, an important element of which is history, along with heritage and country of origin. A prestigious heritage is built and maintained in time and culture by brands that are embedded in historical notions of luxury. As a result of associations with the heritage, brand is perceived as the highest quality, unique and authentic one. Symbolism, heritage and the history of a luxury brand are related to emotional qualities of personal indulgence and self-expression.Purpose of the article: The aim of the article is to verify the importance of the history of the brand in the process of shaping the value of a luxury brand in the perception of consumers.Research methods: A total of 203 valid responses were collected from wealthy respondents declaring monthly income over PLN 20,000 gross. An analysis of the results of the study was carried out, as well as an analysis of the literature.Main findings: In the era of dynamic development of new technologies, unpredictable changes in consumer expectations towards companies and their offers, it turns out that history, heritage and attachment to tradition are highly valued by consumers of luxury goods. They shape a higher level of trust, both in the company’s brand and its products, and increase the consumers purchase willingness. Companies that can boast of long history should undoubtedly communicate it intensively and care about providing consumers not only with basic values related to the product itself, but also symbolic values, which are particularly important for consumer of luxury goods. History and the heritage of a luxury brand constitute one of the essential elements of the brand’s value and should also be treated as such by companies

Time-Fractional Optimal Control of Initial Value Problems on Time Scales

We investigate Optimal Control Problems (OCP) for fractional systems involving fractional-time derivatives on time scales. The fractional-time derivatives and integrals are considered, on time scales, in the Riemann--Liouville sense. By using the Banach fixed point theorem, sufficient conditions for existence and uniqueness of solution to initial value problems described by fractional order differential equations on time scales are known. Here we consider a fractional OCP with a performance index given as a delta-integral function of both state and control variables, with time evolving on an arbitrarily given time scale. Interpreting the Euler--Lagrange first order optimality condition with an adjoint problem, defined by means of right Riemann--Liouville fractional delta derivatives, we obtain an optimality system for the considered fractional OCP. For that, we first prove new fractional integration by parts formulas on time scales.Comment: This is a preprint of a paper accepted for publication as a book chapter with Springer International Publishing AG. Submitted 23/Jan/2019; revised 27-March-2019; accepted 12-April-2019. arXiv admin note: substantial text overlap with arXiv:1508.0075

Cálculo das variações em escalas temporais e aplicações à economia

Doutoramento em MatemáticaWe consider some problems of the calculus of variations on time scales. On the beginning our attention is paid on two inverse extremal problems on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we derive a general form for a variation functional that attains a local minimum at a given point of the vector space. Furthermore, we prove a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation. New and interesting results for the discrete and quantum calculus are obtained as particular cases. Afterwards, we prove Euler-Lagrange type equations and transversality conditions for generalized infinite horizon problems. Next we investigate the composition of a certain scalar function with delta and nabla integrals of a vector valued field. Euler-Lagrange equations in integral form, transversality conditions, and necessary optimality conditions for isoperimetric problems, on an arbitrary time scale, are proved. In the end, two main issues of application of time scales in economic, with interesting results, are presented. In the former case we consider a firm that wants to program its production and investment policies to reach a given production rate and to maximize its future market competitiveness. The model which describes firm activities is studied in two different ways: using classical discretizations; and applying discrete versions of our result on time scales. In the end we compare the cost functional values obtained from those two approaches. The latter problem is more complex and relates to rate of inflation, p, and rate of unemployment, u, which inflict a social loss. Using known relations between p, u, and the expected rate of inflation π, we rewrite the social loss function as a function of π. We present this model in the time scale framework and find an optimal path π that minimizes the total social loss over a given time interval.Consideramos alguns problemas do cálculo das variações em escalas temporais. Primeiramente, demonstramos equações do tipo de Euler-Lagrange e condições de transversalidade para problemas de horizonte infinito generalizados. De seguida, consideramos a composição de uma certa função escalar com os integrais delta e nabla de um campo vetorial. Presta-se atenção a problemas extremais inversos para funcionais variacionais em escalas de tempo arbitrárias. Começamos por demonstrar uma condição necessária para uma equação dinâmica integro-diferencial ser uma equação de Euler-Lagrange. Resultados novos e interessantes para o cálculo discreto e quantum são obtidos como casos particulares. Além disso, usando a equação de Euler-Lagrange e a condição de Legendre fortalecida, obtemos uma forma geral para uma funcional variacional atingir um mínimo local, num determinado ponto do espaço vetorial. No final, duas aplicações interessantes em termos económicos são apresentadas. No primeiro caso, consideramos uma empresa que quer programar as suas políticas de produção e de investimento para alcançar uma determinada taxa de produção e maximizar a sua competitividade no mercado futuro. O outro problema é mais complexo e relaciona a inflação e o desemprego, que inflige uma perda social. A perda social é escrita como uma função da taxa de inflação p e a taxa de desemprego u, com diferentes pesos. Em seguida, usando as relações conhecidas entre p, u, e a taxa de inflação esperada π, reescrevemos a função de perda social como uma função de π. A resposta é obtida através da aplicação do cálculo das variações, a fim de encontrar a curva ótima π que minimiza a perda social total ao longo de um determinado intervalo de tempo

Płeć a postrzeganie luksusu – stosunek kobiet i mężczyzn do produktów luksusowych

The aim of the article is to identify whether and how gender shapes the perception of luxury products and the attitude of young consumers toward this category of goods. The study carried out in the article was conducted among 854 students of two Tri-city universities in November 2017. A questionnaire created by Dubois and Laurent in 1994, including 32 motives shaping respondents’ attitudes to luxury products, has been used. The results of the study present a problem of perception of luxury in the poorly investigated context of gender. If there are differences in the perception of luxury among women and men, learning their source can be important for both science and practice in the field of luxury goods marketing.Celem artykułu jest identyfikacja różnic w postrzeganiu luksusowego charakteru produktu wynikających ze specyficznego podejścia kobiet i mężczyzn do procesów nabywczych. Badanie zrealizowane na potrzeby niniejszego artykułu zostało przeprowadzone wśród 854 studentów dwóch trójmiejskich uczelni wyższych w listopadzie 2017 r. Posłużono się kwestionariuszem stworzonym przez Dubois i Laurent w 1994 r., obejmującym 32 motywy kształtujące stosunek respondentów do produktów luksusowych. Wyniki badania prezentują problem postrzegania luksusu w ubogo zbadanym kontekście płci. Jeśli wśród kobiet i mężczyzn występują różnice w percepcji luksusu, poznanie ich źródła może mieć duże znaczenie zarówno dla nauki, jak i praktyki w zakresie marketingu dóbr luksusowych

Is There Selective Mating in Tetrahymena During Genomic Exclusion? 1

Genomic exclusion is characterized by 2 rounds of mating. If exconjugants from different pairs remated at random after the first mating, we would expect a 1:2:1 ratio for genes present in heterozygous condition in the normal parent. An excess of homozygotes is observed which is similar for 2 different genes, suggesting that 10% of the rematings occur between exconjugants from the same Round 1 pair. Some but not all of these homozygotes can be attributed to a lack of separation of mates after the first round of mating. The rest may result because of differential mortality, induced autogamy or preferential remating.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74657/1/j.1550-7408.1971.tb03365.x.pd

Audyt wykorzystania mediów społecznościowych do komunikacji wartości CSR firm farmaceutycznych

The article discusses the possibilities of communication of CSR values using social media. The characteristics of social media were presented, CSR was defined in the marketing aspect, and marketing communication in social media was defined. The research part of the article is an audit of social media towards communication of CSR values by the five largest Polish companies from the pharmaceutical industry. The research has shown that companies actively carry out marketing communication using social media. Each of the audited companies are present in-analyse various social media. However, the communication of CSR values of the surveyed companies is not at a satisfactory level, because not every one of the largest in the optimal degree realizes the possibilities, social media.)Artykuł omawia możliwości komunikacji wartości CSR z wykorzystaniem mediów społecznościowych. Przedstawiono charakterystykę mediów społecznościowych, zdefiniowano CSR w aspekcie marketingowym, określono możliwości komunikacji marketingowej w mediach społecznościowych. Część badawczą artykułu stanowi audyt mediów społecznościowych w kierunku komunikacji wartości CSR przez pięć największych polskich firm z branży farmaceutycznej. Badania pokazały, że firmy aktywnie prowadzą komunikację marketingową z wykorzystaniem mediów społecznościowych. Każda z audytowanych firm jest obecna w analizowanych mediach społecznościowych. Jednakże komunikacja wartości CSR badanych firm nie jest na zadowalającym poziomie, gdyż nie każda w optymalnym stopniu realizuje możliwości mediów społecznościowych