New Bounds of Weyl Sums

2019 ◽  
Author(s):  
Changhao Chen ◽  
Igor E Shparlinski
Keyword(s):  
Hausdorff Dimension ◽  
Infinite Series ◽  
Dimensional Subspace ◽  
Point Of View ◽  
Orthogonal Projections ◽  
Additional Advantage ◽  
Real Polynomials ◽  
New Ideas ◽  
Technical Innovations ◽  
Lower Dimensional

Abstract We augment the method of Wooley (2016) by some new ideas and in a series of results, improve his metric bounds on the Weyl sums and the discrepancy of fractional parts of real polynomials with partially prescribed coefficients. We also extend these results and ideas to principally new and very general settings of arbitrary orthogonal projections of the vectors of the coefficients $(u_1, \ldots , u_d)$ onto a lower-dimensional subspace. This new point of view has an additional advantage of yielding an upper bound on the Hausdorff dimension of sets of large Weyl sums. Among other technical innovations, we also introduce a “self-improving” approach, which leads to an infinite series of monotonically decreasing bounds, converging to our final result.

scholarly journals Quantum Polar Duality and the Symplectic Camel: A New Geometric Approach to Quantization

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Uncertainty Principle ◽  
Convex Geometry ◽  
Geometric Approach ◽  
Point Of View ◽  
Reconstruction Problem ◽  
Orthogonal Projections ◽  
Topological Version ◽  
Mahler Conjecture ◽  
Quantum Indeterminacy ◽  
Dual Quantum

AbstractWe define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity.

scholarly journals The local structure of the free boundary in the fractional obstacle problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Matteo Focardi ◽  
Emanuele Spadaro
Keyword(s):  
Hausdorff Dimension ◽  
Free Boundary ◽  
Hausdorff Measure ◽  
Local Structure ◽  
Obstacle Problem ◽  
List Type ◽  
Minkowski Content ◽  
Local Finiteness ◽  
Lower Dimensional

AbstractBuilding upon the recent results in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] we provide a thorough description of the free boundary for the solutions to the fractional obstacle problem in {\mathbb{R}^{n+1}} with obstacle function φ (suitably smooth and decaying fast at infinity) up to sets of null {{\mathcal{H}}^{n-1}} measure. In particular, if φ is analytic, the problem reduces to the zero obstacle case dealt with in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] and therefore we retrieve the same results:(i)local finiteness of the {(n-1)}-dimensional Minkowski content of the free boundary (and thus of its Hausdorff measure),(ii){{\mathcal{H}}^{n-1}}-rectifiability of the free boundary,(iii)classification of the frequencies and of the blowups up to a set of Hausdorff dimension at most {(n-2)} in the free boundary.Instead, if {\varphi\in C^{k+1}(\mathbb{R}^{n})}, {k\geq 2}, similar results hold only for distinguished subsets of points in the free boundary where the order of contact of the solution with the obstacle function φ is less than {k+1}.

THE SPECIFICS OF THE DEVELOPMENT OF ONLINE COMMERCE UNDER THE INFLUENCE OF CONSUMER BEHAVIOR OF INTERNET USERS

2021 ◽  
pp. 158-171
Author(s):  
Dmitrii V. Tyurin ◽  
◽  
Aleksandra O. Volkova ◽  
◽  
Keyword(s):  
Consumer Behavior ◽  
Customer Orientation ◽  
Consumer Preferences ◽  
Point Of View ◽  
Practical Skills ◽  
Electronic Format ◽  
Online Commerce ◽  
Goods And Services ◽  
Internet Users ◽  
Technical Innovations

The article presents trends and innovations in the global and Russian markets regarding consumer behavior, analyzes the prospects for the development of online commerce, and suggests various approaches to increasing the share of online store customers and consumer retention in the era of digitalization and e-commerce. In particular, the authors analyzed the specifics of interaction with the audience on the example of a large online platform “Shopping live”. The practical skills of using innovative developments by marketers in terms of the development of mobile consumption of services and goods are demonstrated. The article takes into account the requirements that customers face in connection with the pandemic and forced self-isolation, in particular, the ability to use various technical innovations. It also demonstrates, as modern factors, the experience of practicing marketers, which influenced their work in the electronic format of selling goods and services, and in particular the use of new approaches in communication and customer orientation. The authors formulate approaches to the development of electronic promotion of goods and products of various industries from the point of view of consumer preferences, based on the specifics of the marketing strategy of large marketplaces, such as Wildberries, Aliexpress.

scholarly journals Formation of clusters in cultural heritage – strategies for optimizing resources in museums

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Héctor Moreno - Mendoza ◽  
Agustín Santana - Talavera ◽  
José Molina - González
Keyword(s):  
Cultural Heritage ◽  
Statistical Significance ◽  
Management Strategies ◽  
Cultural Development ◽  
Point Of View ◽  
Content Type ◽  
Homogeneous Groups ◽  
Heritage Sites ◽  
Tourism Product ◽  
New Ideas

PurposeThe purpose of this study is to affirm that it is possible to segment visitors of cultural heritage into homogeneous groups according to a series of characteristics to detect the variables that have statistical significance to identify visitor clusters.Design/methodology/approachFour case studies were selected, where a total of 500 questionnaires were made to visitors. The authors proceeded with cluster analysis using SPSS software to differentiate visitor segments. Four groups of visitors were first identified and which have subsequently been reduced to three, according to several factors.FindingsThe main contributions of this paper are: (1) the segment to which each one of the determinants of the cultural tourism product is dedicated; (2) the variable object of the analysis, i.e. the formation of visitor segments; and (3) the inclusion of less studied variables such as type of accommodation contracted, treatment offered in the museums or entrance price.Research limitations/implicationsThe analysis has been developed in different museums, with different management models, in a specific place. However, the results are generalizable to other places and to other institutions that manage cultural heritage. The implications are management strategies for a sustainable cultural development in institutions of tourism and heritage.Practical implicationsFrom a practical point of view, the results are useful for cultural managers, travel agencies, tour operators, tourism companies or political offices, among others, because they generate new ideas and strategies focused on maximizing the use of the resources of cultural institutions.Social implicationsFor both local and non-local agents, the knowledge of the factors that make up the groups of visitors in the heritage sites represents a strategy in aspects of marketing, promotion and distribution, thus generating capacities for the different intermediaries, and the possibility of negotiating lower prices with better benefits. It is also possible to create new products destined for other publics.Originality/valueThe study is original because this has not been published.

Service Design

2012 ◽  
pp. 211-222
Author(s):  
Satu Miettinen
Keyword(s):  
Design Process ◽  
Design Thinking ◽  
Service Design ◽  
Design Methods ◽  
Point Of View ◽  
Human Interaction ◽  
Service Development ◽  
Service Needs ◽  
New Ideas ◽  
Tourism Service

Service design is establishing itself as a method for developing services and service business. Service needs, new ideas and ways to utilise technology are encountered when the customer and the end user participate in the design process. This chapter focuses on service design methods and the process of how service design can help in innovating customer-orientated service concepts for e-tourism. Service design connects the areas of cultural, social and human interaction. Use of design methods acts as a link between the different views in the service design process. Service design is an emerging field where the terminology and methods are still developing. Mager (2009) has pointed out that the need for service design is evident, as economic development has changed dramatically during the last four decades from manufacturing to provision of information and services. Service design looks at service development from the designer’s point of view. Design thinking has the ability to create concepts, solutions and future service experiences for users.

scholarly journals Social Skills Amongst MMORPG-Gamers: Empirical Study

2018 ◽  
Vol 50 ◽  
pp. 01008 ◽  
Author(s):  
Olga Sergeyeva ◽  
Anna Tsareva ◽  
Nadezhda Zinoveva ◽  
Olga Kononova
Keyword(s):  
Computer Games ◽  
Interpersonal Relations ◽  
Real Life ◽  
Point Of View ◽  
Ordinary People ◽  
Social Culture ◽  
The Real ◽  
New Ideas ◽  
The Impact ◽  
Social Interaction Skills

The research paper addresses the issue of the impact of MMORPGs on social culture and communication skills of individuals. The mainstream discourse about computer games which take individuals away from reality and substitute the real life by the fictional one is complemented by brand new ideas, which affirm that computer games do not substitute but supplement the real life and expand its possibilities. To confirm the presented point of view we use diagnostic questionnaire of interpersonal relations by A.A. Rukavishnikov. This questionnaire is aimed to evaluate typical ways of respondent’s attitude towards other people. At this point we have 43 gamers and 29 non-gamers involved in our research, aged 18 to 57. The comparison of a user and non-user answers gives a bigger view on an overall gaming experience. In the obtained indices we note that there are no fundamental differences between MMORPGs gamers and ordinary people. During research, MMORPGs users have showed many important social interaction skills such as striving to control own actions, collaborate with others, though with a low interest in emotionally charged relationships. Authors discuss the idea about the differences between addiction and fascination among gamers.

Proposal of a guide for talent evaluation and management based on a qualitative and three-staged approach

2020 ◽  
Vol 12 (5) ◽  
pp. 1045-1078
Author(s):  
Atheer Abdullah Mohammed ◽  
Abdul Hafeez Baig ◽  
Raj Gururajan
Keyword(s):  
Higher Education ◽  
Empirical Studies ◽  
Talent Management ◽  
Point Of View ◽  
Content Type ◽  
Individual Interviews ◽  
Strategic Plans ◽  
Talent Retention ◽  
New Ideas ◽  
Value Add

PurposeThe key objective of the study is to understand the best processes that are currently used in managing talent in Australian higher education (AHE) and design a quantitative measurement of talent management processes (TMPs) for the higher education (HE) sector.Design/methodology/approachThe three qualitative multi-method studies that are commonly used in empirical studies, namely, brainstorming, focus group discussions and semi-structured individual interviews were considered. Twenty-three individuals from six Australian universities participated in this study.FindingsThe qualitative study explored three key themes and ten subthemes of TMPs that are used in AHE. These were: (1) talent attraction, (2) talent development and (3) talent retention.Research limitations/implicationsThis study only targeted one country (Australia) and one sector (HE).Practical implicationsThis study offers three major contributions as follows: theoretical, practical and policy aspects. Theoretically, the study provides a value-add to Talent Management (TM) theory through designing a guide (conceptual model) of TMPs for the HE sector. Practically, it collects original qualitative data regarding TM in the HE domain. From a policy point of view, this study adds more debate around adding new ideas to Australian education strategic plans for HE.Originality/valueThis study has a unique methodology because of strengthening the effect of an in-depth case study. For instance, two different techniques were used for data analysis for the same research objective as follows: (1) both manual methods and content analysis software (NVivo 11) and (2) the three-stage approach. Using these techniques for the same purpose in one study can provide greater flexibility to examine the relationship between theory and data.

Dimensions of measures under orthogonal projections

1996 ◽  
Vol 28 (2) ◽  
pp. 344-345
Author(s):  
Martina Zähle
Keyword(s):  
Hausdorff Dimension ◽  
Packing Dimension ◽  
Packing Measure ◽  
Orthogonal Projections

Let dimH, E be the Hausdorff dimension and dimP, E the packing dimension of the subset E of ℝn given by the unique exponent where the corresponding Hausdorff or packing measure of E jumps from infinity to zero.

scholarly journals II. On the principal electric time-constant of a circular disk

1887 ◽  
Vol 42 (251-257) ◽  
pp. 289-296 ◽  
Keyword(s):  
Time Constant ◽  
Infinite Series ◽  
Circular Disk ◽  
Point Of View ◽  
Experimental Point ◽  
Normal Type ◽  
Time Constants ◽  
The One ◽  
Original Strength ◽  
Different Parts

The time-constant for currents of any normal type in a given conductor is the time in which free currents of that type fall to 1/ e of their original strength. In strictness there are for any conductor an infinite series of time-constants, corresponding to the various normal types, but in such a case as that of a coil of wire one of these is very great in comparison with the rest, which belong to types in which the current is in opposite directions in different parts of a section of the wire. And in all cases the time-constant corresponding to the most persistent type which can be present under given circumstances is, of course, the one which is most important from an experimental point of view.

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