Discrete Inclusion Research Articles

Conversion of Isolated Voids into Channel Spaces by Modulating the Stacking Manner of Hydrogen‐Bonded Ladders

1,2,3,4‐Tetrakis(carboxyphenyl)benzene (CPB) forms a predictable ladder‐shaped porous motif through intermolecular hydrogen‐bonding of the carboxy groups. The stacking manner of the ladder motif, on the other hand, cannot be controlled, yielding a crystal structure with discrete inclusion spaces. To modulate the stacking manner, its derivative CPB(OMe) with methoxy substituent groups at 5,6‐positions was synthesized and crystallized to yield a crystalline hydrogen‐bonded organic framework (HOF), in which the ladder motifs are stacking with a different manner to form 1D channel‐shaped inclusion space, instead of discrete ones. Because of the channel structure, removal of the included solvent molecules can be easily conducted, and the resultant activated HOF CPB(OMe)‐a exhibited micropores with BET surface area of 199 m2 g‐1, which is larger than that of the other HOF CPB‐a.

Optimization of Parabolic type Polyhedral discrete, discrete-approximate and differential inclusions

The present paper is devoted to the optimization of parabolic type differential inclusions (DFIs) given by polyhedral set-valued mappings. For this, an auxiliary problem with a polyhedral parabolic discrete inclusion is defined. With the help of locally adjoint mappings and comparison of matrix-coefficients of discrete and discrete-approximate problems, necessary and sufficient optimality conditions for polyhedral-parabolic discrete-approximate inclusions are skilfully constructed. Thus, using the discretization method and the features of the polyhedral nature of the problem, we prove sufficient optimality conditions for a polyhedral parabolic DFI. At the end of the paper, the numerical results are presented.

Influencer as a special type of public opinion leader

The conceptual apparatus of contemporary communicology does not differentiate between the concepts of “opinion leader” and “influencer”. To solve this problem, the author uses a poly-paradigmatic approach using a set of methods: historical and genetic analysis, structural analysis and socio-cultural modelling. As a result of the study, the author offers an author's definition of the concept of “influencer” as a special type of public opinion leader - an independent medium, which spreads its direct influence on the Internet (mainly in social media) through a direct communication channel using new tactics of positioning (the integration of private and public). At the same time, influencer has a significant impact on the target audience, promoting certain ideas (ideological, consumerist, etc.), which ultimately affects the system of norms, values and attitudes of the recipients. The author outlines the limitations of the study and identifies perspective direction related to the need for further substantiation of the above-mentioned media and communication phenomenon. The expediency of addressing the notion of “influencer” from academic positions is shown, and the necessity of its discrete inclusion in the interdisciplinary scientific discourse is substantiated.

Evidence in reproductive medicine

Evidence in reproductive medicine

Optimal control of hyperbolic type discrete and differential inclusions described by the Laplace operator

The paper is devoted to the optimization of a first mixed initial-boundary value problem for hyperbolic differential inclusions (DFIs) with Laplace operator. For this, an auxiliary problem with a hyperbolic discrete inclusion is defined and, using locally conjugate mappings, necessary and sufficient optimality conditions for hyperbolic discrete inclusions are proved. Then, using the method of discretization of hyperbolic DFIs and the already obtained optimality conditions for discrete inclusions, the optimality conditions for the discrete approximate problem are formulated in the form of the Euler-Lagrange type inclusion. Thus, using specially proved equivalence theorems, which are the only tool for constructing Euler-Lagrangian inclusions, we establish sufficient optimality conditions for hyperbolic DFIs. Further, the way of extending the obtained results to the multidimensional case is indicated. To demonstrate the above approach, some linear problems and polyhedral optimization with hyperbolic DFIs are investigated.

Optimal control of parabolic differential inclusions in one space dimension

The paper is devoted to the optimisation of parabolic differential inclusions (DFIs) in a bounded rectangular region. For this, a problem with a parabolic discrete inclusion is defined, which is the main inevitable auxiliary problem. With the help of locally adjoint mappings, necessary and sufficient conditions for the optimality of parabolic discrete inclusions are proved. Then, using the method of discretization of parabolic DFIs and the already obtained optimality conditions for discrete inclusions, the necessary and sufficient conditions for the discrete-approximate problem are formulated in the form of the Euler–Lagrange type inclusion. Thus, using a specially proved equivalence theorem, we establish sufficient optimality conditions for a parabolic DFI. To demonstrate the above approach, some linear problems and polyhedral optimisation with inclusions of parabolic type are investigated. In addition, numerical results are also presented.

On optimality for Mayer type problem governed by a discrete inclusion system with Lipschitzian set-valued mappings

Set-valued optimization which is an extension of vector optimization to set-valued problems is a growing branch of applied mathematics. The application of vector optimization technics to set-valued problems and the investigation of optimality conditions has been of enormous interest in the research of optimization problems. In this paper we have considered a Mayer type problem governed by a discrete inclusion system with Lipschitzian set-valued mappings. A necessary condition for K-optimal solutions of the problem is given via local approximations which is considered the lower and upper tangent cones of a set and the lower derivative of the set-valued mappings.

On the Relative Bicentralizer Flows and the Relative Flow of Weights of Inclusions of Factors of Type III$_1$

We show that the relative bicentralizer flow and the relative flow of weights are isomorphic for an inclusion of injective factors of type III1 with finite index, or an irreducible discrete inclusion whose small algebra is an injective factor of type III _1 .

Discrete inclusion models for reinforced composites: Comparative performance analysis and modeling challenges

We report the results of a comparative analysis of mesh independent discrete inclusion models and point out some shortcomings of classical approaches in the approximation of the strain field across an inclusion (artificial continuity) and the slip profile along an inclusion (oscillatory behavior). We also present novel embedded reinforcement models based on partition of unity enrichment strategies, adaptive h-refinement, and order/regularity extensions. These novel models are assessed by means of mesh convergence studies and it is shown that they improve the quality of the solution by significantly decreasing local spurious oscillations in the slip profile along an inclusion.

Realizations of algebra objects and discrete subfactors

We give a characterization of extremal irreducible discrete subfactors (N⊆M,E) where N is type II1 in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where the morphisms for discrete inclusions are normal N−N bilinear ucp maps which preserve the state τ∘E, and the morphisms for W*-algebra objects are categorical ucp morphisms.As an application, we get a well-behaved notion of the standard invariant of an extremal irreducible discrete subfactor, together with a subfactor reconstruction theorem. Thus our equivalence provides many new examples of discrete inclusions (N⊆M,E), in particular, examples where M is type III coming from non Kac-type discrete quantum groups and associated module W*-categories. Finally, we obtain a Galois correspondence between intermediate subfactors of an extremal irreducible discrete inclusion and intermediate W*-algebra objects.

DATA PROCESSING SYSTEM OF DIGITAL TEMPERATURE SENSORS IN ORDER TO OPTIMIZE ENERGY COSTS OF SMART HOME

The aim of this work is the development of heat regime management of smart home, which satisfies conditions of comfort and economy. The investigation deals with the problem of minimization of payment of consumed energy for heating of smart home. Saving is possible due to the different power supply tariffs. Cheaper payment was implemented with the use of optimization time diagram of discrete inclusion of heater in different cost of energy tariffs. It was installed values of minimum Emin and maximum Emax energy possible for house in condition of permanent inclusion of heater. Time step of introduced energy was egual to one hour. The model of smart house represents system of linear algebraic eduations, solution of such give set possible chart options of discrete inclusions of heater. From a set of option was selected the case that answers minimum of payment of heating. It was created the calculation program by Python with using library Pyomo. The code of program is given in the appendix

Maximum set of initial conditions for the problem of weak practical stability of a discrete inclusion

We study the properties of the maximum set for practical weak stability of discrete inclusions. The properties of boundary and interior points and compactness of the set of initial data are proved. The Minkowski function, the inverse Minkowski function, and the support function are obtained for discrete linear inclusions.

On the maximum principle for discrete inclusions

We consider an optimization problem given by a discrete inclusion, whose trajec- tories are constrained to closed sets. Necessary optimality conditions in the form of the maximum principle and in terms of local generalized derived cones of constraints are obtained.

2D transient filtration model for aluminum

A two-dimensional, transient mathematical model representing the behavior of a deep-bed filter was developed. The flow and mass fraction equations are solved using CFX™ commercial code. The rate equation representing the inclusion deposition and re-entrainment is incorporated into a model as a source term of the mass fraction equation. The resistance of the bed is calculated using the pressure drop calculated by the Ergun equation. The model takes into account all the major physical processes occurring during filtration. For each time step, the model calculates the inclusion concentrations remaining in the liquid and deposited on the filter media. It updates the bed porosity and bed particle size as the inclusions deposit. The model can use either an average inclusion size or a discrete inclusion size distribution. It is also possible to assign different densities to different inclusion sizes if an inclusion distribution is used.The model was applied to various industrial filter geometries. The results were compared with available plant data. The mechanisms involved in aluminum filtration are not all well known. However, the model seems to successfully predict the flow and recirculation patterns as well as the inclusion deposition patterns observed in the plant filters. After model validation, a parametric study was carried out to determine the effects of different model parameters on the filtration performance.

Magma yield stress and permeability: Insights from multiphase percolation theory

Magmas often contain multiple interacting phases of embedded solid and gas inclusions. Multiphase percolation theory provides a means of modeling assemblies of these different classes of magmatic inclusions in a simple, yet powerful way. Like its single phase counterpart, multiphase percolation theory describes the connectivity of discrete inclusion assemblies as a function of phase topology. In addition, multiphase percolation employs basic laws to distinguish separate classes of objects and is characterized by its dependency on the order in which the different phases appear. This paper examines two applications of multiphase percolation theory: the first considers how the presence of bubble inclusions influences yield stress onset and growth in a magma's crystal network; the second examines the effect of bi-modal bubble-size distributions on magma permeability. We find that the presence of bubbles induces crystal clustering, thereby 1) reducing the percolation threshold, or critical crystal volume fraction, ϕ c , at which the crystals form a space-spanning network providing a minimum yield stress, and 2) resulting in a larger yield stress for a given crystal volume fraction above ϕ c . This increase in the yield stress of the crystal network may also occur when crystal clusters are formed due to processes other than bubble formation, such as heterogeneous crystallization, synneusis, and heterogeneity due to deformation or flow. Further, we find that bimodal bubble size distributions can significantly affect the permeability of the system beyond the percolation threshold. This study thus demonstrates that larger-scale structures and topologies, as well as the order in which different phases appear, can have significant effects on macroscopic properties in multiphase materials.

Minimum principle and controllability for multiparameter discrete inclusions via derived cones

We consider a multiparameter discrete inclusion and we prove that the reachable set of a certain variational multiparameter discrete inclusion is a derived cone in the sense of Hestenes to the reachable set of the discrete inclusion. This result allows to obtain sufficient conditions for local controllability along a reference trajectory and a new proof of the minimum principle for an optimization problem given by a multiparameter discrete inclusion with endpoint constraints.

Compact global attractors of discrete inclusions

The paper is dedicated to the study of the problem of the existence of compact global attractors of discrete inclusions and to the description of its structure. We consider a family of continuous mappings of a metric space W into itself, and ( W , f i ) i ∈ I is the family of discrete dynamical systems. On the metric space W we consider a discrete inclusion (1) u t + 1 ∈ F ( u t ) associated with M ≔ { f i : i ∈ I } , where F ( u ) = { f ( u ) : f ∈ M } for all u ∈ W . We give sufficient conditions (the family of maps M is contracting in the extended sense) for the existence of a compact global attractor of (1). If the family M consists of a finite number of maps, then the corresponding compact global attractor is chaotic. We study this problem in the framework of non-autonomous dynamical systems (cocyles).

Formation of morphologically similar globular aggregates from diverse aggregation-prone proteins in mammalian cells

Huntington's disease is a progressive neurodegenerative disorder caused by a polyglutamine repeat expansion in the first exon of the huntingtin (Htt) protein. N-terminal Htt peptides with polyglutamine tracts in the pathological range (51-122 glutamines) form high-molecular-weight protein aggregates with fibrillar morphology in vitro, and they form discrete inclusion bodies in a cell-culture model. However, in some studies, formation of discrete Htt inclusions does not correlate well with cell death. We coexpressed N-terminal Htt fragments containing 91 glutamines fused to different affinity tags in HEK293 cells, and we isolated small aggregates by double sequential-affinity chromatography to assure the isolation of multimeric molecules. Transmission electron microscopy and atomic force microscopy revealed the isolated aggregates as globules or clusters of globules 4-50 nm in diameter without any detectable fibrillar species. Because small nonfibrillar oligomers, not mature fibrils, recently have been suggested to be the principal cytotoxic species in neurodegenerative disease, these Htt globular aggregates formed in cells may represent the pathogenic form of mutant Htt.

Discrete Second Order Inclusions

New existence results are presented for the second order discrete inclusion ( 2 y ( i -1) ] F ( i , y ( i )), i ] {1,…, T }, with y (0)= y ( T +1)=0. Our technique involves using fixed point theory for multivalued upper semicontinuous maps from the literature.

The generalized spectral radius and extremal norms

The generalized spectral radius, also known under the name of joint spectral radius, or (after taking logarithms) maximal Lyapunov exponent of a discrete inclusion is examined. We present a new proof for a result of Barabanov, which states that for irreducible sets of matrices an extremal norm always exists. This approach lends itself easily to the analysis of further properties of the generalized spectral radius. We prove that the generalized spectral radius is locally Lipschitz continuous on the space of compact irreducible sets of matrices and show a strict monotonicity property of the generalized spectral radius. Sufficient conditions for the existence of extremal norms are obtained.