F. M. Dostoevsky – great human-lover, expert in human, well-wisher of human, sage and visionary

The philosophical meaning and humanistic pathos of F. M. Dostoevsky’s work is revealed, embodied in his novels and «The diary of a writer». The depth and bottomlessness of a person – the writer’s symbol of faith – are presented. The philosophical, ethical and psychological generalisations of the Russian writer are presented as the central point of the metaphysical problem of man as a personality, her life, quest, suffering, love, faith. The theory of F. M. Dostoevsky’s creativity is reconstructed, for which a person is interesting when he embarks on only his own, individual path, but passing which, highlights something typical for the entire people, its historical fate and destiny, strength and weakness. Only in the personal identity of each person is the general identity of the nation embodied; to defend in any circumstances the honour of the Russian man and the honour of his people – this is precisely what the citizen writer saw as the vocation of Russia. The dialectic of love, freedom, beauty and immortality as components of the meaning of human life is revealed. Against this background, death is presented as an inevitable moral lesson, the meaning of which is to sharpen the feelings of love and humility: love for man and humility before God. This understanding of life and death is opposed by demonic, a phenomenon devoid of love and humility. For F. M. Dostoevsky, who had an acute presentiment of future social upheavals in Russia and Europe, devilry is embodied in the revolutionary ideas of seizing power, restructuring society and man according to the patterns of political leaders who only yearn for domination and submission of others to their will. The prophecies and premonitions made by F. M. Dostoevsky about the future of Russia and its place in world history are characterised. The emphasis is on the writer’s rejection of the revolution as a fratricidal war and the denial of the viability of communist ideas and ideals. Only religiously coloured humanism can be opposed to these gloomy forecasts: a better future will come when people, based on the implementation of the main Christian thesis, to love their neighbour as themselves, will be able to unite into a single harmonious whole or the paradise of Christ.

Some New Inequalities on Generalization of Hermite-Hadamard and Bullen Type Inequalities, Applications to Trapezoidal and Midpoint Formula

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.

Taxing Identity: Theory and Evidence From Early Islam

A ruler who does not identify with a social group, whether on religious, ethnic, cultural, or socioeconomic grounds, is confronted with a trade‐off between taking advantage of the out‐group population's eagerness to maintain its identity and inducing it to “comply” (conversion, quitting, exodus, or any other way to accommodate the ruler's own identity). This paper first nests economists' extraction model, in which rulers are revenue‐maximizers, within a more general identity‐based model, in which rulers care also about inducing people to lose their identity, both in a static and an evolving environment. This paper then constructs novel data sources to test the implications of both models in the context of Egypt's conversion to Islam between 641 and 1170. The evidence supports the identity‐based model.

Consumer cultural identity: local and global cultural identities and measurement implications

Purpose The purpose of this paper is to offer a framework for considering the interplay between local (national) and global (world-based) identities and consumption practices with attention to various conceptualizations and measurements of consumer cultural identity. Design/methodology/approach This is a conceptual paper reviewing major works on consumer cultural identities and offering a framework for future considerations of the interplay between global and local identities. Findings The framework identifies two dimensions which underlie consumer cultural identity conceptualizations and measurements: first, consumer engagement with globalization–localization discourses, and second, more general identity beliefs vs consumption-based identity beliefs. Clustering and categorical measure approaches (vs a compensatory approach) are preferred for identifying and exploring global/local/glocal and unengaged consumer cultural identity segments. Research foci should guide use of global and/or local general identity vs consumption-based identity beliefs as predictors of marketplace outcomes or as segmentation variables. Research limitations/implications The conceptualization of consumer cultural identity is based on Berry et al.’s (1986) early work on acculturation and Arnett’s (2002) bicultural identity theorizing, and thus the authors acknowledge four consumer segments, those with: stronger global (weaker local) identity, stronger local (weaker global) identity, strong global and local identities and those unengaged with global–local discourses. The authors review measurement approaches to examine consumer cultural identity and determine that categorical and clustering (vs compensatory) approaches are consistent with the conceptualization of consumer cultural identity segments. Practical implications International marketers can gain insights into major conceptualizations and measurements of consumer cultural identity, and understand the advantages and limitations of different measurement approaches. The authors highlight two important dimensions underlying cultural identity that demand managers’ attention and consideration for strategic decisions. Social implications – this paper brings attention to various conceptualizations and measures of consumer cultural identity, highlighting the need to further examine differences between various cultural identity segments, specifically the unengaged consumers and glocally engaged consumers. Originality/value The paper provides a broadened lens to understanding conceptualizations and measurements of consumer cultural identity, identifying two dimensions underlying consumer cultural identity: consumer engagement with globalization–localization discourses, and more general identity beliefs vs consumption-based identity beliefs.

Some integral inequalities for multiplicatively geometrically P-functions

In this manuscript, by using a general identity for differentiable functions we can obtain new estimates on a generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolute value at certain power are multiplicatively geometrically P-functions. Some applications to special means of real numbers are also given.

Pre-Wiring and Pre-Training: What Does a Neural Network Need to Learn Truly General Identity Rules?

In an influential paper (“Rule Learning by Seven-Month-Old Infants”), Marcus, Vijayan, Rao and Vishton claimed that connectionist models cannot account for human success at learning tasks that involved generalization of abstract knowledge such as grammatical rules. This claim triggered a heated debate, centered mostly around variants of the Simple Recurrent Network model. In our work, we revisit this unresolved debate and analyze the underlying issues from a different perspective. We argue that, in order to simulate human-like learning of grammatical rules, a neural network model should not be used as a tabula rasa, but rather, the initial wiring of the neural connections and the experience acquired prior to the actual task should be incorporated into the model. We present two methods that aim to provide such initial state: a manipulation of the initial connections of the network in a cognitively plausible manner (concretely, by implementing a “delay-line” memory), and a pre-training algorithm that incrementally challenges the network with novel stimuli. We implement such techniques in an Echo State Network (ESN), and we show that only when combining both techniques the ESN is able to learn truly general identity rules. Finally, we discuss the relation between these cognitively motivated techniques and recent advances in Deep Learning.

A new form of the quintuple product identity and its application

We give a new form of the quintuple product identity. As a direct application of this new form a simple proof of known identities of Ramanujan and also new identities for other well known continued fractions are given. We also give and prove a general identity for (q3m; q3m)?.

Runs in coin tossing: a general approach for deriving distributions for functionals

We take a fresh look at the classical problem of runs in a sequence of independent and identically distributed coin tosses and derive a general identity/recursion which can be used to compute (joint) distributions of functionals of run types. This generalizes and unifies already existing approaches. We give several examples, derive asymptotics, and pose some further questions.