Analytic Normalized Solutions of 2D Fractional Saint-Venant Equations of a Complex Variable

Saint-Venant equations describe the flow below a pressure surface in a fluid. We aim to generalize this class of equations using fractional calculus of a complex variable. We deal with a fractional integral operator type Prabhakar operator in the open unit disk. We formulate the extended operator in a linear convolution operator with a normalized function to study some important geometric behaviors. A class of integral inequalities is investigated involving special functions. The upper bound of the suggested operator is computed by using the Fox-Wright function, for a class of convex functions and univalent functions. Moreover, as an application, we determine the upper bound of the generalized fractional 2-dimensional Saint-Venant equations (2D-SVE) of diffusive wave including the difference of bed slope.

Cardinality Estimation of an SQL Query Using Recursive Neural Networks

To learn complex interactions between predicates and accurately estimate the cardinality of an SQL query, we develop a novel framework based on recursive tree-structured neural networks, which take into account the natural properties of logical expressions: compositionality and n-ary associativity. The proposed architecture is an extension of MSCN (multi-set convolutional network) for queries containing both conjunction and disjunction operators. The goal is to represent an arbitrary logical expression in a continuous vector space by combining sub-expression vectors according to the operator type. We compared the proposed approach with the histogram-based approach on the real-world dataset and showed that our approach significantly outperforms histograms with a large margin.

Asymptotically autonomous robustness of random attractors for a class of weakly dissipative stochastic wave equations on unbounded domains

This paper is concerned with the asymptotic behaviour of solutions to a class of non-autonomous stochastic nonlinear wave equations with dispersive and viscosity dissipative terms driven by operator-type noise defined on the entire space $\mathbb {R}^n$ . The existence, uniqueness, time-semi-uniform compactness and asymptotically autonomous robustness of pullback random attractors are proved in $H^1(\mathbb {R}^n)\times H^1(\mathbb {R}^n)$ when the growth rate of the nonlinearity has a subcritical range, the density of the noise is suitably controllable, and the time-dependent force converges to a time-independent function in some sense. The main difficulty to establish the time-semi-uniform pullback asymptotic compactness of the solutions in $H^1(\mathbb {R}^n)\times H^1(\mathbb {R}^n)$ is caused by the lack of compact Sobolev embeddings on $\mathbb {R}^n$ , as well as the weak dissipativeness of the equations is surmounted at light of the idea of uniform tail-estimates and a spectral decomposition approach. The measurability of random attractors is proved by using an argument which considers two attracting universes developed by Wang and Li (Phys. D 382: 46–57, 2018).

The moderating effect of operator type: the impact of information technology (IT) expenditures on hotels’ operating performance

Purpose This study aims to examine how operator type moderates the relationship between hotel information technology (IT) expenditures and operating performance. Design/methodology/approach By adapting and extending O’Neill et al.’s (2008) and Hua et al.’s (2015) research, this study constructed an empirical model and tested proposed hypotheses, with Newey and West (1994) errors computed to accommodate potential heteroscedasticity and autocorrelation issues. Findings Operator type moderates the impact of hotel IT expenditures on operating performance. In particular, it appears that the operator type of franchising exerts a stronger moderating effect compared with other operator types explored. Practical implications This study, as the first of its kind, shows that the choice of operator type shapes how a hotel can effectively use IT expenditures to improve operating performance. This finding can be beneficial for hotel owners when making operator type decisions. In addition, operator type moderates the direct impact of IT expenditures on revenues and gross operating income. This study’s results show that franchised hotels seem to use IT expenditures more effectively compared with independently owned hotels. Originality/value This study contributes both theoretically and practically to understand how operator type moderates the relationship between IT expenditures and hotel performance. The research outcome provides a more holistic view that governs the relationships between IT expenditures, operator type and operating performance.

NEW APPROACHES IN OPTIMIZATION OF CALCULATION OF WAVE FIELDS DIRECTLY RELATED TO THE SELECTED TARGET AREA OF SEISMIC RESPONSE

The article describes the method of calculating the wave field of reflected waves of a certain type of re-reflection from localized target objects. A special feature of the method is the combination of the wave field continuation operator calculated by means of layer-by-layer recalculation based on the Kirchhoff integral and the finite-difference operator of reflected waves. Parameterization of the wave field continuation operator type is determined on the basis of the frame effective depth-velocity model. The research is carried out by Seismotech, Ltd under the grant support of "Skolkovo" Foundation.

Local Users, Consortial Providers: Seeking Points of Dissatisfaction with a Collaborative Virtual Reference Service

Objective – Researchers at an academic library consortium examined whether the service model, staffing choices, and policies of its chat reference service were associated with user dissatisfaction, aiming to identify areas where the collaboration is successful and areas which could be improved. Methods – The researchers examined transcripts, metadata, and survey results from 473 chat interactions originating from 13 universities between June and December 2016. Transcripts were coded for user, operator, and question type; mismatches between the chat operator and user’s institutions, and reveals of such a mismatch; how busy the shift was; proximity to the end of a shift or service closure; and reveals of such aspects of scheduling. Chi-square tests and a binary logistic regression were performed to compare variables to user dissatisfaction. Results – There were no significant relationships between user dissatisfaction and user type, question type, institutional mismatch, busy shifts, chats initiated near the end of a shift or service closure time, or reveals about aspects of scheduling. However, revealing an institutional mismatch was correlated with user dissatisfaction. Operator type was also a significant variable; users expressed less dissatisfaction with graduate student staff hired by the consortium. Conclusions – The study largely reaffirmed the consortium’s service model, staffing practices, and policies. Users are not dissatisfied with the service received from chat operators at partner institutions, or by service provided by non-librarians. Current policies for scheduling, handling shift changes, and service closure are appropriate, but best practices related to disclosing institutional mismatches may need to be changed. This exercise demonstrates that institutions can trust the consortium with their local users’ needs, and underscores the need for periodic service review.

IDEA OF ARCHITECTURE OF A MULTIPROCESSOR COMPUTER M-10 AND THEIR IMPLEMENTATION IN MODERN COMPUTING PLATFORMS (IN SMALL FORMS)

The article is devoted to the design of high‑performance computing devices for parallel processing of information. The problem of increasing the productivity of computing facilities by one or several orders of magnitude is considered on the example of the high‑ performance electronic computer M‑10, which was created in the 1970s at the NIIVK. If in a conventional computer, the method of processing numbers is given by commands, then in M‑10, the methods for processing a function were specified by operators taken from functional analysis. At the same time, the possibility of parallel processing of an entire information line appeared. Such systems began to be called «functional operator type machines». The main ideas presented in the article may be of interest to developers of specialized machines of the new generation, as well as engineers involved in the creation of high‑performance computing devices using technologies of computing platforms.

Application measure of noncompactness and operator type contraction for solvability of an infinite system of differential equations in lp-space

The aim of this paper is to obtain existence results for an infinite system of second order differential equations in the sequence space lp for 1 ? p < ? with the help of a technique associated with measures of noncompactness and contractive condition of operator type. We also provide some illustrative examples in support of our existence theorems.

Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains

This article is motivated by the quantitative study of the exponential growth of Markov-driven bifurcating processes [see Hervé et al., ESAIM: PS 23 (2019) 584–606]. In this respect, a key property is the multiplicative ergodicity, which deals with the asymptotic behaviour of some Laplace-type transform of nonnegative additive functional of a Markov chain. We establish a spectral version of this multiplicative ergodicity property in a general framework. Our approach is based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including linear autoregressive models. In these two examples the operator-type assumptions reduce to some expected finite moment conditions on the functional (no exponential moment conditions are assumed in this work).