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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.

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.

The goal is to find a systemic information assembling mechanism, which would describe not only a human being's way of organizing the accepted information but also the general information regularities of this process, applied to different information objects.

Mathematical formalism of Informational Macrodynamics is employed for system modeling of the object's regularities and the main systemic mechanisms. The developed systemic assembling mechanism joins a chaotic oscillation of incoming information frequencies, initiating a chaotic resonance, into a cooperative attractor. A chain of sequentially built attractors generates a collective information dynamic network (IN), whose hierarchy models the multiple information contributions. An information structure of the IN node's attractors is memorized by the key‐lock connections of resonance frequencies.

The results indicate that formalized functions of the assembling cooperative information mechanisms represent a general attribute of a system.

A wide area of applications includes behavior analysis, cognition, artificial intelligence, data organization and management, social systems, and education.

The considered results bring together the formal systemic model of the regularities of collective macrodynamics and the mathematical evaluation of a complex individual's behavior in a collective environment.

Tourism spot or point-of-interest (POI) recommendation has become a common service in people's daily life. The purpose of this paper is to model users' check-in history in order to predict a set of locations that a user may soon visit.

The authors proposed a novel learning-based method, the pattern-based dual learning POI recommendation system as a solution to consider users' interests and the uniformity of popular POI patterns when making recommendations. Differing from traditional long short-term memory (LSTM), a new users’ regularity–POIs’ popularity patterns long short-term memory (UP-LSTM) model was developed to concurrently combine the behaviors of a specific user and common users.

The authors introduced the concept of dual learning for POI recommendation. Several performance evaluations were conducted on real-life mobility data sets to demonstrate the effectiveness and practicability of POI recommendations. The metrics such as hit rate, precision, recall and F-measure were used to measure the capability of ranking and precise prediction of the proposed model over all baselines. The experimental results indicated that the proposed UP-LSTM model consistently outperformed the state-of-the-art models in all metrics by a large margin.

This study contributes to the existing literature by incorporating a novel pattern–based technique to analyze how the popularity of POIs affects the next move of a particular user. Also, the authors have proposed an effective fusing scheme to boost the prediction performance in the proposed UP-LSTM model. The experimental results and discussions indicate that the combination of the user's regularity and the POIs’ popularity patterns in PDLRec could significantly enhance the performance of POI recommendation.

The article investigates the incidence and regularity of performance of marketing‐mix activities in Third World business contexts. The results support a relatively high level of incidence and regularity of performance of marketing‐mix activities — thus implying their “applicability”. However, the results suggest that corporate factors influence the performance of marketing‐mix activities.

Science of systems requires a specific and constructive mathematical model and language, which describe jointly such systemic categories as adaptation, self‐organization, complexity, evolution, and bring the applied tools for building a system model for each specific object of a diverse nature. This formalism should be connected directly with a world of information and computer applications of systemic model, developed for a particular object. The considered information systems theory (IST) is aimed at building a bridge between the mathematical systemic formalism and information technologies to develop a constructive systemic model of revealing information regularities and specific information code for each object.

To fulfill this goal and the considered systems' definition, the IST joins two main concepts: unified information description of interacted flows, initiated by the sources of different nature, with common information language and systems modeling methodology, applied to distinct interdisciplinary objects; general system's information formalism for building the model, which allows expressing mathematically the system's regularities and main systemic mechanisms.

The formalism of informational macrodynamics (IMD), based of the minimax variational principle, reveals the system model's main layers: microlevel stochastics, macrolevel dynamics, hierarchical dynamic network (IN) of information structures, its minimal logic, and optimal code of communication language, generated by the IN hierarchy, dynamics, and geometry. The system's complex dynamics originate information geometry and evolution with the functional information mechanisms of ordering, cooperation, mutation, stability, diversity, adaptation, self‐organization, and the double helix's genetic code.

The developed IMD's theoretical computer‐based methodology and the software has been applied to such areas as technology, communications, computer science, intelligent processes, biology, economy, management, and other nonphysical and physical subjects.

The IMD's macrodynamics of uncertainties connect randomness and regularities, stochastic and determinism, reversibility and irreversibility, symmetry and asymmetry, stability and instability, structurization and stochastization, order and disorder, as a result of micro‐macrolevel's interactions for an open system, when the external environment can change the model's structure.

This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.