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A theorem of Henry Helson shows that for every ordinary Dirichlet series ∑ ann-s with a square summable sequence (an) of coefficients, almost all vertical limits ∑ anχ(n)n-s, where χ : ℕ → 𝕋 is a completely multiplicative arithmetic function, converge on the right half-plane. We survey recent improvements and extensions of this result within Hardy spaces of Dirichlet series - relating it with some classical work of Bohr, Banach, Carleson-Hunt, Cesàro, Hardy-Littlewood, Hardy-Riesz, Menchoff-Rademacher and Riemann. [ABSTRACT FROM AUTHOR]

Topic strength is an important hotspot in topic research. The evolution of topic strength not only indicates emerging new topics, but also helps us to determine whether a topic will produce some fluctuation of topic strength over time. Thus, topic strength analysis can provide significant findings in public opinion monitoring and user personalization. In this paper, we present an LDA-based topic strength analysis approach. We take topic quality into our topic strength consideration by combining local LDA and global LDA. For empirical studies, we use three data sets in real applications: film critic data of "A Chinese Odyssey" in Douban Movies, corruption news data in Sina News, and public paper data. Compared to existing approaches, experimental results show that our proposed approach can obtain better results of topic strength analysis in detecting the time of event topic occurrences and distinguishing different types of topics, and it can be used to monitor the occurrences of public opinions and the changes of public concerns. [ABSTRACT FROM AUTHOR]

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We study the degree of compactness of composition operators C φ acting on weighted Hilbert spaces of entire functions, which include (i) the space of entire Dirichlet series, (ii) the space of entire power series, and (iii) the Fock space (we must have φ ( z ) = a z + b , and it is known that C φ is compact if and only if | a | < 1 ). More precisely, the sequence ( a n ) of approximation numbers of C φ is investigated: for (i), we give the exact formula for ( a n ) , while for (ii) and (iii) we give upper and lower estimates for a n , showing that a n behaves like | a | n up to a subexponential factor. In particular, C φ belongs to all Schatten classes S p , p > 0 as soon as it is compact. [ABSTRACT FROM AUTHOR]

The concept of digital entrepreneurial ecosystems (DEEs) has been developed to systemically analyze entrepreneurship in the digital age. Research on DEEs is, however, still dispersed, and there exists ambiguity in this relevant field. With the aim of creating a more comprehensive understanding of DEEs, we conduct a systematic literature review that outlines the current state of research and consolidates the literature at the intersection of digital entrepreneurship and entrepreneurial ecosystems. Since DEEs have been explored from different perspectives and given the adoption of various attributes, we propose a conceptual framework presenting a set of characterizations corresponding to principal ecosystem attributes. By offering a range of characteristics, our framework provides an inclusive picture of the different possible types of DEEs, offering promising avenues for future research. • ▪ The concept of DEEs subsumes digital entrepreneurship and entrepreneurial ecosystems • ▪ We propose a conceptual framework presenting a set of characterizations of DEEs • ▪ We present a two-by-two typology that delineates four forms of DEEs • ▪ We highlight important future avenues of research exploring DEE attributes [ABSTRACT FROM AUTHOR]

Autonomous vehicles (AVs) will bring considerable benefits to individuals and society, while the process of AVs' popularity may not always be smooth. Sometimes crashes are unavoidable, which could hinder the widespread acceptance of AVs. Although previous studies have investigated factors that affect AV acceptance, few of them pay attention to the impact of accidents and not to mention quantitative analysis. This study aims to explore what the public is really concerned about the AV crash and whether it significantly affects the public's behavioral intention to use AVs utilizing a multi-method analytical approach, including latent Dirichlet allocation, structural equation model, and Bayesian network. We employed a qualitative exploratory analysis to identify the topics of social media data about AV crashes and proposed an integrated framework using variables originating from topics. We introduced perceived severity in AV acceptance research to cater to the context of AV crashes. The findings reveal how trust, attitude, knowledge, perceived risk, media exposure, and perceived severity affect the public acceptance of AVs and how differences exist between full automation and driver assistance. This research helps to provide theoretical contributions and practical implications to reduce the negative effect of AV crashes and improve public acceptance of AVs. • This paper investigates public perceptions of autonomous vehicles (AVs) after an accident. • A hybrid method combining social media and a questionnaire survey aims to get the real public concern about AV crashes. • We proposed an integrated framework using variables originating from social media data. • This study reveals the mechanism of consumers' adoption of AV technology. [ABSTRACT FROM AUTHOR]

In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense. It is observed that the obtained results are a natural generalization of the integer order derivative. Some interesting properties of the fractional derivative of the Riemann zeta function are also investigated to show that there is a chaotic decay to zero (in the Gaussian plane) and a promising expression as a complex power series. [ABSTRACT FROM AUTHOR]

We are concerned here with Dirichlet series f ( s ) = 1 + ∑ n = 2 ∞ c ( n ) n s which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f ( s ) = 2 s q 1 / 2 − s π s − 1 Γ ( 1 − s ) ( sin π 2 ( s + κ ) ) f ( 1 − s ) , but for which the Riemann hypothesis is false. Indeed we show that the zeros of such functions are ubiquitous in the complex plane. [ABSTRACT FROM AUTHOR]

Abstract: Classification and prediction of users’ whereabouts patterns is important for many emerging ubiquitous computing applications. Latent Dirichlet Allocation (LDA) is a powerful mechanism to extract recurrent behaviors and high-level patterns (called topics) from mobility data in an unsupervised manner. One drawback of LDA is that it is difficult to give meaningful and usable labels to the extracted topics. We present a methodology to automatically classify the topic with meaningful labels so as to support their use in applications. We also present a topic prediction mechanism to infer user’s future whereabouts on the basis of the extracted topics. Both these two mechanisms are tested and evaluated using the Reality Mining dataset consisting of a large set of continuous data on human behavior. [Copyright &y& Elsevier]

Abstract: We investigate the behavior of fronts in bistable activator–inhibitor systems near Dirichlet boundaries. In particular, analytical and numerical investigations are performed for a FitzHugh–Nagumo dynamics. Conditions for a bound state and for a rebound of fronts are formulated. We also show fronts which oscillate between two reflecting boundaries. If additive noise is applied, nucleation of pairwise fronts near the boundary is observed. The front running towards the boundary is reflected there, and a pulse-like sequence of fronts propagating away from the boundary is established. Thus, noise and the boundary play the role of a pacemaker of a permanent progression of fronts. The sequence becomes highly ordered at optimal noise level. We also present examples of a two dimensional generalization of this noisy pacemaker. [Copyright &y& Elsevier]

Abstract: The present paper deals with the study on a class of entire functions represented by Dirichlet series whose coefficients belong to a commutative Banach algebra with identity. We consider a class of such series which satisfy certain conditions and establish some results. [Copyright &y& Elsevier]

Abstract: By (extended) Wiener–Ikehara theory, the prime-pair conjectures are equivalent to simple pole-type boundary behavior of corresponding Dirichlet series. Under a weak Riemann-type hypothesis, the boundary behavior of weighted sums of the Dirichlet series can be expressed in terms of the behavior of certain double sums . The latter involve the complex zeros of and depend in an essential way on their differences. Extended prime-pair conjectures are true if and only if the sums have good boundary behavior. Equivalently, a more general sum (with real ) should have a boundary function (or distribution) that is well-behaved, apart from a pole with residue of period . [ could be determined for .] [Copyright &y& Elsevier]

It is shown that there are domains that maximise the expected lifetime of Brownian motion over all simply connected domains of given inradius and all starting points. [ABSTRACT FROM AUTHOR]

Sbimura has studied the structure of the Hecke ring R(Δ,Γ) in the case Γ = SLn(ℤ) and Δ ⊇ Γ is a subsemigroup of G =GLn (ℚ). Let p be a prime and let Γ = GLn (ℤ p) ⊆ Δ ⊆ G = GLn (ℚ p), where Δ is a semigroup. In this paper, we shall determine the structure of the Hecke ring R(Δ, Γ) and its some properties. [ABSTRACT FROM AUTHOR]