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The purpose of this paper is to investigate the L^p‐maximal regularity for the abstract incomplete second order problem.

First, the paper gives the definition of the L^p‐maximal regularity for incomplete second‐order Cauchy problems and lists their basic properties based on Chill and Srivastava's recent work for completing second order problem. Second, the paper establishes its characterization by means of Fourier multiplier and the operator‐sum theorem. Finally, it considers an application to quasilinear systems by the regularity and linearization techniques.

Two criteria of L^p‐maximal regularity are obtained, and the existence of the local solution for the second order quasilinear problem is given. In addition, the connection on maximal regularity between second order problems with initial values and that with periodic problems is investigated. A perturbation result is given.

The maximal regularity is an important tool in the theory of non‐linear differential equations. The results obtained in this paper are universal because the operator is not necessarily the generator of a cosine operator function. Using this unifying approach it is possible to clarify the L^p‐maximal regularity and the existence of the solution for some systems described by partial differential equations, such as wave equations.

Purpose: The purpose of the chapter is to determine the regularities and tendencies of decision making in business systems by the example of modern Russia.

Methodology: The method of logical analysis (analysis of causal connections) and the method of dynamic analysis of development of socioeconomic systems are used. These methods are applied with the current statistical and analytical information. The information and analytical basis of the research is the materials of the Federal State Statistics Service for 2018.

Conclusions: The factors of functioning and development of modern business systems, related to development of E-commerce, liberalization of state regulation of business systems, growth of their competition and corporate responsibility, change of technological mode, and crisis are determined. Influence of these factors on managerial decisions is connected to reduction of resource provision of business systems, accessibility of new managerial tools, complication of made decisions (growth of the number of accessible decisions), growth of the number of new technologies of decision making, and increase of the risk component of decisions. Regularities and tendencies of decision making are determined: striving for saving resources during decision making, more active usage of new managerial tools during decision making, striving for acceleration of the process of making of more complicated managerial decisions, more active usage of new technologies during decision making, and striving for minimization of risks of made decisions.

Originality/value: It is substantiated that the determined regularities and tendencies of decision making lead to increase of contradiction during making of managerial decisions in modern business systems, connected to growth of complexity of this process and simultaneous reduction of resources and time that are accessible to business managers. In order to solve this contradiction, it is necessary to implement cardinal changes into the process of making of managerial decisions in modern business systems, which allow – with minimum managerial cost – determining multiple alternative variants of solutions of the whole specter of current problems of a business system and comparing them as to mutually excluding criteria, thus making complex decisions.

This paper aims to explore the moderating impact of four moderators, namely, retailer brand strength, customer’s perceived purchase regularity, gender and purchase channel (online and offline) on the relationship between relationship marketing investments (RMIs) and customer gratitude, and customer gratitude and customer loyalty. The context of research is the purchase of a high-involvement product by Indian customers.

This study adapts Huang RMIs-Gratitude-Loyalty model and empirically validates the associated hypotheses using structural equation modeling. Data is collected through the survey method.

The study (N = 385) results suggest a significant impact of preferential treatment and interpersonal communication investments on customer’s feeling of gratitude toward the retailer and, consequently, on loyalty. Purchase channel, gender and, to a lesser extent, customer perceived regularity each moderates the relationships between marketing investment and gratitude, and that between gratitude and loyalty; surprisingly, retailer brand is not a significant moderator.

Future research can factor in the impact of loyalty program on the proposed relationships.

This research offers helpful guidelines for retailers, especially for those who currently have a multichannel presence and invest or plan to invest in relationship marketing to obtain benefits from customer loyalty.

This investigation explores not only the relevance of RMIs–gratitude–loyalty model in the Indian retail context but also the influence of moderating variables on the retailers’ efforts of gaining consumer loyalty.

To better understand the online reviews and help potential consumers, businessmen and product manufacturers effectively obtain users’ evaluation on product aspects, this paper aims to explore the distribution regularities of users’ attention and sentiment on product aspects from the temporal perspective of online reviews.

Temporal characteristics of online reviews (purchase time, review time and time intervals between purchase time and review time), similar attributes clustering and attribute-level sentiment computing technologies are used based on more than 340k smartphone reviews of three products from JD.COM (a famous online shopping platform in China) to explore the distribution regularities of users’ attention and sentiment on product aspects in this paper.

The empirical results show that a power-law distribution can fit users’ attention on product aspects, and the reviews posted in short time intervals contain more product aspects. Besides, the results show that the values of users’ sentiment on product aspects are significantly higher/lower in short time intervals which contribute to judging the advantages and weaknesses of a product.

This paper cannot acquire online reviews for more products with temporal characteristics to verify the findings because of the restriction on reviews crawling by the shopping platforms.

This work reveals the distribution regularities of users’ attention and sentiment on product aspects, which is of great significance in assisting decision-making, optimizing review presentation and improving the shopping experience.

The purpose of this study is to obtain the numerical as well as regularity results for the nonlinear elliptic set of equations arising in the study of fluid flow in microchannel induced by the pressure in the presence of interfacial electrokinetic effects.

For the numerical study, the authors implemented traditional FDM approach, and for the regularity results they used the classical energy estimates. The interfacial electrokinetic effects result in an additional source term in classical momentum equation, hence affecting the characteristics of the flow and heat transfer. The sinusoidal temperature variation is assumed on side walls.

The results were obtained for various combinations of physical parameters appearing in the governing equations. This study concludes that in the presence of electric double layer, the average heat transfer rate reduces along with larger values of Reynolds number. It is observed that the heat transfer increases with the increase in amplitude ratio and phase deviation. The flow behavior and heat transfer rate inside the microchannel are also strongly affected by the presence of κ (kappa).

To the best of the authors’ knowledge, the problem of heat transfer through microchannel in combination with sinusoidal temperature variation at boundary with electric double layer effects has not been considered previously. Hence, this paper focuses on the influence of the sinusoidal boundary temperature distributions on both sidewalls of a rectangular microchannel through parallel plates with electrokinetic effects on the pressure-driven laminar flow. In addition, a detailed mathematical analysis is also to be carried out to verify the regularity of this model with the proposed boundary conditions. The study used the classical energy method to get the regularity results.

The purpose of this paper is to investigate the approximation performance of a family of piecewise rational polynomial shape functions, which are enriched by a set of monomials of order p to obtain high order approximations. To numerically demonstrate the features of the enriched approximation some examples on the mechanical elastic response and free‐vibration of axisymmetric plates and shells are carried out.

The global approximation is based on a particular family of weight function, which is defined on the parametric domain of the element, ξ∈[−1,1], resulting in shape functions with compact support, which have regularity C₀^k,k=0,2,4… in the global domain Σ. The PU shape functions are enriched by a set of monomials of order p to obtain high order approximation spaces.

Based on the numerical results of elastic axisymmetric plates and shells, it is demonstrated that the proposed methodology produces satisfactory results in terms of keeping the ill‐conditioning of the system of equations under accepted levels. Comparisons are established between linear and Hermitian shape functions showing similar results. The observed results for the free‐vibration problem of plates and shells show the potential of the proposed approximation space.

In this paper the formulation is limited to the modeling of axisymmetric plate and shell problems. However, it can be applied to model other problems where the high regularity of the approximation is required.

The paper presents an alternative approach to construct partition of unity shape functions based on a particular family of weight function.