Search

Given a geometric structure on $\mathbb{R}^{n}$ with $n$ even (e.g. Euclidean, symplectic, Minkowski, pseudo-Euclidean), we analyze the set of points inside the domain of definition of an arbitrary given $\mathcal{C}^1$ vector field, where the value of the vector field equals the value of the left/right gradient--like vector field of some fixed $\mathcal{C}^2$ potential function, although a non-integrability condition holds at each such a point. Particular examples of gradient--like vector fields include the class of gradient vector fields with respect to Euclidean or pseudo-Euclidean inner products, and the class of Hamiltonian vector fields associated to symplectic structures on $\mathbb{R}^{n}$ (with $n$ even). The main result of this article provides a geometric version of the main result of [1]., Comment: 7 pages

In this paper, optimal methods of approximation of some geophysical fields, in particular gravitational and thermal fields, are considered. A review of the results on this problem is presented. An algorithm of approximation for the multidimensional thermal fields described by a heat equation with constant coefficients is developed. For this, classes of functions including the solutions of heat equations are introduced, and continuous splines uniformly approximating the functions from the classes in the whole domain of definition are constructed. Upper bounds for the Kolmogorov widths of these classes of functions are given. For a wider class of the thus introduced classes of functions, a lower estimate of the Kolmogorov width is presented.

This paper redefines the Shape of numbers, makes it more natural and concise, and the domain of definition is extended to ring. The inconvenient PCHG() and PH() are removed. The concept of subsets is also removed. The new definition can be used to calculate ∑n-0N-1Πi-1M (Ki+n×Di) ∑ni,j-0j-N-1Πi-1M (Ki+ni,j×Di), ni,j≤ni+1,j or ni,j=ni+1,j; Ki,Di∈ring. Three forms corresponding to three calculation methods are obtained. They can be used as a powerful tool for analysis. Some of the conclusions are: 1) Expressions and properties of two kinds of Stirling number, Lah number and Eulerian number; 2) Expression of power sum of natural numbers; 3) Vandermonde identity, Norlund identity; 4) New congruence and new proof of Wilson theorem; 5) ∑n-1P-1≡0 MOD P2, P>3; 6) ∑C-0C-M-1(-1)M-1-C∑PM(PS)-M,PB(PS)-CMIN(PS)=1.

α-1,3-Glucanase from Streptomyces thermodiastaticus HF3-3 (Agl-ST) has been classified in the glycoside hydrolase (GH) family 87. Agl-ST is a multi-modular domain consisting of an N-terminal β-sandwich domain (β-SW), a catalytic domain, an uncharacterized domain (UC), and a C-terminal discoidin domain (DS). Although Agl-ST did not hydrolyze α-1,4-glycosidic bonds, its amino acid sequence is more similar to GH87 mycodextranase than to α-1,3-glucanase. It might be categorized into a new subfamily of GH87. In this study, we investigated the function of the domains. Several fusion proteins of domains with green fluorescence protein (GFP) were constructed to clarify the function of each domain. The results showed that β-SW and DS domains played a role in binding α-1,3-glucan and enhancing the hydrolysis of α-1,3-glucan. The binding domains, β-SW and DS, also showed binding activity toward xylan, although it was lower than that for α-1,3-glucan. The combination of β-SW and DS domains demonstrated high binding and hydrolysis activities of Agl-ST toward α-1,3-glucan, whereas the catalytic domain showed only a catalytic function. The binding domains also achieved effective binding and hydrolysis of α-1,3-glucan in the cell wall complex of Schizophyllum commune.

The present paper proposes a fast and easy to implement level set topology optimization method that is able to adjust the complexity of resulting configurations. While the existing methods solve a large system of linear equations, the proposed method applies a density filter to the level set function in order to smoothen the optimized configurations. Considering the proposed method, the minimum total potential energy problem and optimum design problem of compliant mechanism will be studied in the present study. In topology optimization methods, the topological derivative determines the criteria of removing/adding material from/to the domain of definition of the problem. We utilize the definition of topological derivative to measure the sensitivity of a given objective function when an infinite small hole is inserted at an arbitrary location of the domain. It is shown that a first-order stress field appears in the topological derivative. Moreover, a comprehensive Airy stress function is proposed in order to solve the boundary value problem that governs the appeared first-order stress field. Finally, a simple MATLAB implementation is provided to confirm the effectiveness and utility of the proposed method.

In this paper, triple reciprocity method (TRM) is employed to transform the unknown function's domain integral appearing in boundary integral equation (BIE) to boundary integrals. The three-dimensional interior Helmholtz equation is represented as a Poisson equation with an unknown function in the right-hand side. The fundamental solution of Laplace equation is used to derive the BIE and there is a domain integral containing unknown field function in the BIE. The triple reciprocity method (TRM) is used to transform this domain integral to boundary integrals. The improved triple reciprocity approximation (TRA) is used to approximate the unknown domain function and solve the high-order derivatives of it virtually. Employing the reciprocity theory, the domain integral is transferred into the boundary integrals containing the unknown field function. Finally, the BIE can be solved without internal cells. The proposed formulas can be employed to treat the domain integral containing time derivatives of unknown variable, both known and unknown functions and other similar types. Three numerical examples are presented to demonstrate the efficiency and accuracy of the proposed formulas. Results show that TRM can solve the BIE containing unknown function's domain integral efficiently and accurately.

The cognitive style has an important role in determining the characteristics of students on the conceptualization. One of the two types of cognitive styles are field independent (FI) and field dependent (FD). The purpose of this study was to identify the form of conceptual misconceptions about limit and their causes. This type of research is a case study. The data was obtained through interviews based on the conceptual problem-solving tasks. Correspondents used in this study were from first-year college students (95 people) who were studied at Universitas Jambi. The results showed that (1) FI forms of students' misconceptions, namely: misconceptions about interpreting the concept of function limit and function conditions which have limits, such as: left limit and right limit. This problem occurred due to incomplete reasoning and wrong intuition. The other result of this research was to obtain (2) FD forms of students' misconception, namely, (a) misconceptions about prerequisite material: drawing graphs of functions, misconceptions about determining the domain of a function, misconceptions about definitions and forms of function notations, misconceptions about determining function values on function graphs (b) misconceptions about the concept of limits: misconceptions about interpreting the concept of limits in a function, the function requirements (left limit, right limit) and misconceptions about understanding the meaning which is close to the limit function (limit-x) approaching infinity.

We study homeomorphisms of Riemannian manifolds with unbounded characteristic such that the inverse mappings satisfy the Poletsky-type inequality. It is established that their families are equicontinuous if the function Q which is related to the Poletsky inequality and is responsible for a distortion of the modulus, is integrable in the given domain, here the original manifold is connected and the domain of definition and the range of values of mappings have compact closures.

The work is devoted to the development of a method for approximating discontinuous functions using the operator of interlination of two variables functions. These operators reconstruction functions ( possibly approximately ) from their known traces on a given line system. It is such experimental data that are used in remote remote methods, in particular, in computed tomography. That is, they provide an opportunity to build operators whose integrals over the indicated lines (linear integrals) will be equal to the integrals of the function being restored. So, interlination is a mathematical apparatus naturally associated with the task of restoring the characteristics of objects from their known projections. There are many practically important scientific and technical branches in which objects of research are mathematically described by values that have a discontinuity. Such objects often arise also in tasks using remote methods. To date, there is no general theory of descriptions of phenomena and processes described by discontinuous functions. The paper constructs and explores discontinuous interlination operators for approximating discontinuous functions of two variables according to its known traces ( projections ) on a system of lines using arbitrary triangular elements. On the basis of the created spline- interlinants, a method is constructed for approximating functions that have discontinuities of the first kind and whose domain of definition is divided into triangular elements. Moreover, the constructed discontinuous structures include, as a special case, the classic continuous interlination splines. The experimental data are one-sided traces of a function on a system of given lines; precisely such data are used in tomography. The paper presents theorems on interlining properties and errors of constructed discontinuous structures. The constructed approximation method allows us to approximate the discontinuous function, avoiding the Gibbs phenomenon. The examples confirming the effectiveness of the proposed method are considered. The proposed method for approximating discontinuous functions can be used for mathematical modeling of discontinuous processes in medical, geological, space and other studies.

HR business partner, Business Excellence are some buzzwords in the industry nowadays. Profitability and efficiency are being driven through various strategic initiatives aligned to the vision of the organization. Customer satisfaction is now being replaced by customer delight. Organizations are taking steps ahead of voice of customer. The consumer insights are thoroughly analyzed and interpreted. Data analytics is not restricted to only finance and operation functions but are widely used across the support functions along with line functions. Human resource is now considered as an asset. Organizations are also trying to find out ways to capitalize the full potential of human asset. Various tools and methodologies are paving its way to bring efficient human resource management practices. Six Sigma is one of the tools, which is booming into the application space of Human Resource Management. Six Sigma is being considered as a business process and is helping the in shaping and improving their bottom line by designing and monitoring various activities to reduce the defects.

Grant n. 19-01-00451 UID/MAT/00297/2020 We propose a stochastic algorithm for global optimisation of a regular function, possibly unbounded, defined on a bounded set with regular boundary; a function that attains its extremum in the boundary of its domain of definition. The algorithm is determined by a diffusion process that is associated with the function by means of a strictly elliptic operator that ensures an adequate maximum principle. In order to preclude the algorithm to be trapped in a local extremum, we add a pure random search step to the algorithm. We show that an adequate procedure of parallelisation of the algorithm can increase the rate of convergence, thus superseding the main drawback of the addition of the pure random search step. publishersversion published

Significance Single amino acid changes causative of neurologic disease often map to the cross-β forming regions of low-complexity (LC) domains. All such mutations studied to date lead to enhanced avidity of cross-β interactions. The LC domain of the fused in sarcoma (FUS) RNA binding protein contains three different regions that are capable of forming labile cross-β interactions. Here we describe the perplexing effect of amyotrophic lateral sclerosis (ALS)-causing mutations localized to the LC domain of FUS to substantially weaken its ability to form one of its three cross-β interactions. An understanding of how these mutations abet uncontrolled polymerization of the FUS LC domain may represent an important clue as to how LC domains achieve their proper biological function., The low-complexity (LC) domain of the fused in sarcoma (FUS) RNA binding protein self-associates in a manner causing phase separation from an aqueous environment. Incubation of the FUS LC domain under physiologically normal conditions of salt and pH leads to rapid formation of liquid-like droplets that mature into a gel-like state. Both examples of phase separation have enabled reductionist biochemical assays allowing discovery of an N-terminal region of 57 residues that assembles into a labile, cross-β structure. Here we provide evidence of a nonoverlapping, C-terminal region of the FUS LC domain that also forms specific cross-β interactions. We propose that biologic function of the FUS LC domain may operate via the mutually exclusive use of these N- and C-terminal cross-β cores. Neurodegenerative disease–causing mutations in the FUS LC domain are shown to imbalance the two cross-β cores, offering an unanticipated concept of LC domain function and dysfunction.

We study the mappings of metric spaces that distort the moduli of the families of paths according to the Poletsky inequality. In the case where the mapped domain is a weakly flat space, and the enveloping metric space admits a weak sphericalization, the equicontinuity of the corresponding families of inverse mappings is established. Under some additional conditions, the equicontinuity of the corresponding families of mappings in the closure of their domain of definition has proved.

In this paper, we prove that a radially lower semicontinuous function of one variable, defined on some interval, is pseudoconvex, if and only if its domain of definition can be split into three parts such that the function is strictly monotone decreasing without stationary points over the first subinterval, it is constant over the second one, and it is strictly monotone increasing without stationary points over the third subinterval. Each one or two of these parts may be empty or degenerate into a single point. The proof of this property is easy, when the function is differentiable. We consider functions, which are pseudoconvex with respect to the lower Dini directional derivative. This result follows from some known claims, but our theorem is a shot, directed to the target. We apply this characterization to obtain a complete characterization of strictly pseudoconvex functions. We also derive the respective results, when the function is radially lower semicontinuous in a real linear space. Several applications of the characterization are provided. A result due to Diewert, Avriel and Zang is extended to radially continuous functions.

The relaxation of monotonicity requirements is a trend in the theory of aggregation functions. In the recent literature, we can find several relaxed forms of monotonicity, such as weak, directional, cone, ordered directional and strengthened directional monotonicity. All these forms of monotonicity are global properties in the sense that they are imposed for all the points in the domain of a function . In this work, we introduce a local notion of monotonicity called pointwise directional monotonicity, or directional monotonicity at a point. Based on this concept, we characterize all the previously defined notions of monotonicity and, in the final part of the paper, we present some geometric aspects of the global weaker forms of monotonicity, stressing their relations and singularities .

This technical note focuses on positive definite functions defined on compact sets which contain the origin in their interior. It provides a class- $$\mathcal{K}$$ function bounding inequality for the given positive definite function which is satisfied for its entire domain of definition. An application of the result is also given to analyze the stability of perturbed nonlinear systems whose nominal parts contain an asymptotically stable equilibrium point at the origin.

The aim of this paper is to study the operator (ddc▪)q ∧ T on some classes of plurisubharmonic (psh) functions, which are not necessary bounded, where T is a positive closed current of bidimension (q, q) on an open set Ω of ℂn. The author introduces two classes $${\cal F}_p^T\left( {\rm{\Omega }} \right)$$ and $${\cal E}_p^T\left( {\rm{\Omega }} \right)$$ and shows first that they belong to the domain of definition of the operator (ddc▪)q ∧ T. Then the author proves that all functions that belong to these classes are CT-quasi-continuous and that the comparison principle is valid for them.

International audience; A challenge faced by peptidases is the recognition of highly diverse substrates. A feature of some peptidase families is the capacity to specifically use post-translationally added glycans present on their protein substrates as a recognition determinant. This is ultimately critical to enabling peptide bond hydrolysis. This class of enzyme is also frequently large and architecturally sophisticated. However, the molecular details underpinning glycan recognition by these O -glycopeptidases, the importance of these interactions, and the functional roles of their ancillary domains remain unclear. Here, using the Clostridium perfringens ZmpA, ZmpB, and ZmpC M60 peptidases as model proteins, we provide structural and functional insight into how these intricate proteins recognize glycans as part of catalytic and noncatalytic substrate recognition. Structural, kinetic, and mutagenic analyses support the key role of glycan recognition within the M60 domain catalytic site, though they point to ZmpA as an apparently inactive enzyme. Wider examination of the Zmp domain content reveals noncatalytic carbohydrate binding as a feature of these proteins. The complete three-dimensional structure of ZmpB provides rare insight into the overall molecular organization of a highly multimodular enzyme and reveals how the interplay of individual domain function may influence biological activity. O -glycopeptidases frequently occur in host-adapted microbes that inhabit or attack mucus layers. Therefore, we anticipate that these results will be fundamental to informing more detailed models of how the glycoproteins that are abundant in mucus are destroyed as part of pathogenic processes or liberated as energy sources during normal commensal lifestyles.

The pathogenic consequences of 369 unique human HsMLH1 missense variants has been hampered by the lack of a detailed function in mismatch repair (MMR). Here single-molecule images show that HsMSH2-HsMSH6 provides a platform for HsMLH1-HsPMS2 to form a stable sliding clamp on mismatched DNA. The mechanics of sliding clamp progression solves a significant operational puzzle in MMR and provides explicit predictions for the distribution of clinically relevant HsMLH1 missense mutations.

In this chapter, the basic and advanced problems of functions, algebra of functions, and inverse functions are presented. To help students study the chapter in the most efficient way, the problems are categorized in different levels based on their difficulty levels (easy, normal, and hard) and calculation amounts (small, normal, and large). Moreover, the problems are ordered from the easiest problem with the smallest computations to the most difficult problems with the largest calculations.

A new principle of mathematical models creation for the technical and other objects which are characterized by essential nonlinearity of interdependence of variables is substantiated. It is shown that the use of special analytical functions with a number of unique properties for the multiplicative transformation of fragmented mathematical models that approximate certain parts of the modeled dependencies allows us to obtain new functions that are analytically isolated in their domain of definition. The analyticity of these functions makes it possible additively to combine them into a single analytical function that approximates the simulated dependence in the entire area of its description. In this case, the total approximation error of the mathematical model of the studied object does not exceed the largest error of fragmentary approximating functions. The unique properties of multiplicatively isolating functions provide an almost “seamless” additive union of fragments. This chapter is dedicated to the study and proof of these properties, which are illustrated by examples.

In this chapter, the problems of the seventh chapter are fully solved, in detail, step-by-step, and with different methods.

Let us recall the main definitions associated with the classical Fourier transform known from the course of mathematical analysis. The Fourier transform is one of the central methods of modern applied mathematics [1, 2]. Consider a function \(s:\mathbb {R}\rightarrow \mathbb {C}\). Let s(t) be absolutely integrable on its domain of definition, that is \(\int \limits _{-\infty }^\infty |s(t)| dt

Zona Pellucida domain (ZP) proteins are critical components of the body’s external-most protective layers, apical extracellular matrices (aECMs). Although their loss or dysfunction is associated with many diseases, it remains unclear how ZP proteins assemble in aECMs. Current models suggest that ZP proteins polymerize via their ZPn subdomains, while ZPc subdomains modulate ZPn behavior. Using the model organism C. elegans, we investigated the aECM assembly of one ZP protein, LET-653, which shapes several tubes. Contrary to prevailing models, we find that LET-653 localizes and functions via its ZPc domain. Furthermore, we show that ZPc domain function requires cleavage at the LET-653 C-terminus, likely in part to relieve inhibition of the ZPc by the ZPn domain, but also to promote some other aspect of ZPc domain function. In vitro, the ZPc, but not ZPn, domain bound crystalline aggregates. These data offer a new model for ZP function whereby the ZPc domain is primarily responsible for matrix incorporation and tissue shaping., Author summary Apical extracellular matrices line and shape external body surfaces and the insides of biological tubes. Common components of apical matrices are Zona Pellucida domain (ZP) proteins. These proteins are typically thought to form fibrillar polymers via their N-terminal ZPn subdomains, but how they do so in vivo, and whether other assembly mechanisms occur, is not well understood. Here we use the model organism C. elegans to investigate how one ZP protein, LET-653, assembles into a matrix layer. We visualized the matrix assembly of the LET-653 ZP domain in vivo and demonstrated that, unlike previously described ZP proteins, LET-653 functions and incorporates into matrix via its C-terminal ZPc subdomain. This study identifies new mechanisms by which ZP proteins can assemble into matrices.

International audience; Multi-fidelity approaches combine different models built on a scarce but accurate data-set (high-fidelity data-set), and a large but approximate one (low-fidelity data-set) in order to improve the prediction accuracy. Gaussian Processes (GPs) are one of the popular approaches to exhibit the correlations between these different fidelity levels. Deep Gaussian Processes (DGPs) that are functional compositions of GPs have also been adapted to multi-fidelity using the Multi-Fidelity Deep Gaussian process model (MF-DGP). This model increases the expressive power compared to GPs by considering non-linear correlations between fidelities within a Bayesian framework. However, these multi-fidelity methods consider only the case where the inputs of the different fidelity models are defined over the same domain of definition (e.g., same variables, same dimensions). However, due to simplification in the modeling of the low-fidelity, some variables may be omitted or a different parametrization may be used compared to the high-fidelity model. In this paper, Deep Gaussian Processes for multi-fidelity (MF-DGP) are extended to the case where a different parametrization is used for each fidelity. The performance of the proposed multifidelity modeling technique is assessed on analytical test cases and on structural and aerodynamic real physical problems.

International audience; This article studies the kinetic dynamics of the rock-paper-scissors binary game. We first prove existence and uniqueness of the solution of the kinetic equation and subsequently we prove the rigorous derivation of the quasi-invariant limit for two meaningful choices of the domain of definition of the independent variables. We notice that the domain of definition of the problem plays a crucial role and heavily influences the behavior of the solution. The rigorous proof of the relaxation limit does not need the use of entropy estimates for ensuring compactness.

A Riemann surface can be thought as the domain of definition of a holomorphic function f that has been continued analytically as far as such continuations can be carried out. In general this is not a domain in the previous sense, i.e. a subset of the plane. Rather it is a complex manifold of one (complex) dimension that projects locally into \(\mathbb {C}\).

To design a digital control system, a z -domain transfer function or difference equation model of the controller that meets given design specifications, is seeked. The controller model can be obtained from the model of an analog controller that meets the same design specifications. Alternatively, the digital controller can be designed in the z -domain using procedures that are almost identical to s -domain analog controller design. This chapter elucidates both these approaches. It begins with an explanation of the z -domain root locus and describes the method of sketching the z -domain root locus for a digital control system or obtaining it using MATLAB. This approach is based on the relation between any time function and its s -domain poles and zeros. If the time function is sampled and the resulting sequence is z- transformed, the z -transform contains information about the transformed time sequence and the original time function. The poles of the z -domain function can therefore be used to characterize the sequence, and possibly the sampled continuous time function, without inverse z -transformation. However, this latter characterization is generally more difficult than characterization based on the s -domain functions.

We have already mentioned that the integral of a holomorphic function over a path connecting given two points is unchanged under deformations of the path as long as it remains within the domain of definition of the function. In this chapter, among other things, we will rigorously prove this statement. To begin with, we give a precise definition of a deformation of a path.

Let V be a complex variety in a bounded domain D ⊂ C n . We study the domain of definition for the Monge-Ampere operator of plurisubharmonic functions on V. We are also concerned with the existence and uniqueness of the Monge-Ampere equation on certain class of plurisubharmonic functions.

Plant nucleotide-binding leucine-rich repeat receptors (NLRs) are intracellular pathogen receptors whose N-terminal domains are integral to signal transduction after perception of a pathogen-derived effector protein. The two major plant NLR classes are defined by the presence of either a Toll/interleukin-1 receptor (TIR) or a coiled-coil (CC) domain at their N-terminus (TNLs and CNLs). Our knowledge of how CC domains function in plant CNLs lags behind that of how TIR domains function in plant TNLs. CNLs are the most abundant class of NLRs in monocotyledonous plants, and further research is required to understand the molecular mechanisms of how these domains contribute to disease resistance in cereal crops. Previous studies of CC domains have revealed functional diversity, making categorization difficult, which in turn makes experimental design for assaying function challenging. In this review, we summarize the current understanding of CC domain function in plant CNLs, highlighting the differences in modes of action and structure. To aid experimental design in exploring CC domain function, we present a ‘best-practice’ guide to designing constructs through use of sequence and secondary structure comparisons and discuss the relevant assays for investigating CC domain function. Finally, we discuss whether using homology modeling is useful to describe putative CC domain function in CNLs through parallels with the functions of previously characterized helical adaptor proteins.

Plasma ADAMTS13 circulates in a folded conformation that is stabilized by an interaction between the central Spacer domain and the C-terminal CUB (complement components C1r and C1s, sea urchin protein Uegf, and bone morphogenetic protein-1) domains. Binding of ADAMTS13 to the VWF D4(-CK) domains or to certain activating murine monoclonal antibodies (mAbs) induces a structural change that extends ADAMTS13 into an open conformation that enhances its function. The objective was to characterize the mechanism by which conformational activation enhances ADAMTS13-mediated proteolysis of VWF. The activating effects of a novel anti-Spacer (3E4) and the anti-CUB1 (17G2) mAbs on the kinetics of proteolysis of VWF A2 domain fragments by ADAMTS13 were analyzed. mAb-induced conformational changes in ADAMTS13 were investigated by enzyme-linked immunosorbent assay. Both mAbs enhanced ADAMTS13 catalytic efficiency (kcat/Km) by ∼twofold (3E4: 2.0-fold; 17G2: 1.8-fold). Contrary to previous hypotheses, ADAMTS13 activation was not mediated through exposure of the Spacer or cysteine-rich domain exosites. Kinetic analyses revealed that mAb-induced conformational extension of ADAMTS13 enhances the proteolytic function of the metalloprotease domain (kcat), rather than augmenting substrate binding (Km). A conformational effect on the metalloprotease domain was further corroborated by the finding that incubation of ADAMTS13 with either mAb exposed a cryptic epitope in the metalloprotease domain that is normally concealed when ADAMTS13 is in a closed conformation. We show for the first time that the primary mechanism of mAb-induced conformational activation of ADAMTS13 is not a consequence of functional exosite exposure. Rather, our data are consistent with an allosteric activation mechanism on the metalloprotease domain that augments active site function. ispartof: BLOOD ADVANCES vol:4 issue:6 pages:1072-1080 ispartof: location:United States status: published

We study linear systems of ordinary differential equations of higher order with an identically singular matrix at the higher derivative of the required vector-valued function in the domain of definition. We give definitions of the index and singular points for these systems, formulate the conditions of solvability, and deduce a formula for the general solution. The algorithms for finding the index and singular points are presented.

International audience; This paper presents a novel method to construct a family of piecewise affine control Lyapunov functions. Unlike most of existing methods which require the contractivity of their domain of definition, the proposed control Lyapunov functions are defined over a so-called N −step controllable set, which is known not to be contractive. Accordingly, a robust control design procedure is presented which only requires solving a linear programming problem at each sampling time. The construction is finally illustrated via a numerical example.

A nodal domain of a function is a maximally connected subset of the domain for which the function does not change sign. Courant's nodal domain theorem gives a bound on the number of nodal domains of eigenfunctions of elliptic operators. In particular, the k-th eigenfunction contains no more than k nodal domains. We prove a generalization of Courant's theorem to discrete graphs. Namely, we show that for the k-th eigenvalue of a generalized Laplacian of a discrete graph, there exists a set of corresponding eigenvectors such that each eigenvector can be decomposed into at most k nodal domains. In addition, we show this set to be of co-dimension zero with respect to the entire eigenspace.

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

In the paper, we propose a method for proving the unconditional basis property of eigen- and associated functions of an integro-differential operator defined on a nondense domain of definition. In particular, we obtain a new simpler proof of the unconditional basis property of eigenand associated functions of the spectral Orr–Sommerfeld problem, well-known in hydromechanics, which reduces to the eigenvalue problem for the operator under study.

This paper is a survey of results involving the Schwarzian derivative and depending on the geometry of the image of a domain under a holomorphic map. The author's results obtained previously by using the theory of condenser capacity and symmetrization constitute the core of the paper. Inequalities for univalent and multivalent functions are considered both at interior and at boundary points of the domain of definition. Auxiliary results and proofs of some of the theorems are presented. Bibliography: 52 titles.

In this paper, we consider the analytical pricing of European path-independent options under the CGMY model, which is a particular type of pure jump L e ´ vy process, and agrees well with many observed properties of the real market data by allowing the diffusions and jumps to have both finite and infinite activity and variation. It is shown that, under this model, the option price is governed by a fractional partial differential equation (FPDE) with both the left-side and right-side spatial-fractional derivatives. In comparison to derivatives of integer order, fractional derivatives at a point not only involve properties of the function at that particular point, but also the information of the function in a certain subset of the entire domain of definition. This “globalness” of the fractional derivatives has added an additional degree of difficulty when either analytical methods or numerical solutions are attempted. Albeit difficult, we still have managed to derive an explicit closed-form analytical solution for European options under the CGMY model. Based on our solution, the asymptotic behaviors of the option price and the put-call parity under the CGMY model are further discussed. Practically, a reliable numerical evaluation technique for the current formula is proposed. With the numerical results, some analyses of impacts of four key parameters of the CGMY model on European option prices are also provided.

We propose a time value related decision function to treat a classical option pricing problem raised by Hutchinson-Lo-Poggio. In numerical experiments, the new decision function significantly improves the original model of Hutchinson-Lo-Poggio with faster convergence and better generalization performance. By proving a novel universal approximation theorem, we show that our decision function rather than Hutchinson-Lo-Poggio's can be approximated on the entire domain of definition by neural networks. Thus the experimental results are partially explained by the representation properties of networks., To appear in IJCNN 2021

The restriction of the input set in the form of a positive cone of the space is not always correct. For instance, while studying the organ of vision, people are limited not only to positive, but also to radiation with not very high energies, because excessively intense can disturb the visual organ. In this particular case, a convex body of a linear space is a fairly acceptable model of the set of input signals. Therefore, in this section we consider linear predicates with this domain of definition.

International audience; Many theorems in mathematics require a real function to be continuous over the domain under consideration. In particular the Brouwer fixed point theorem and the mean value theorem underlie many interval methods like Newton operators for solving numerical constraint satisfaction problems or global optimization problems. Since the continuity property collapses when the function is not defined at some point it is then important to check whether the function is defined everywhere in a given domain. We introduce here an interval branch-and-contract algorithm that rigorously approximate the domain of definition of a fac-torable function within a box. The proposed approach mainly relies on interval contractors applied to the domain constraints and their negations stemming from the expression of the function.

The late (L) domain sequence used by mouse mammary tumor virus (MMTV) remains undefined. Similar to other L domain-containing proteins, MMTV p8 and p14 NC proteins are monoubiquitinated, suggesting L domain function. Site-directed mutagenesis of p8, PLPPV, and p14 NC , PLPPL, sequences in MMTV Gag revealed a requirement only for the PLPPV sequence in virion release in a position-dependent manner. Electron microscopy of a defective Gag mutant confirmed an L domain budding defect morphology. The equine infectious anemia virus (EIAV) YPDL core L domain sequence and PLPPV provided L domain function in reciprocal MMTV and EIAV Gag exchange mutants, respectively. Alanine scanning of the PLPPV sequence revealed a strict requirement for the valine residue but only minor requirements for any one of the other residues. Thus, PLPPV provides MMTV L domain function, representing a fourth type of retroviral L domain that enables MMTV Gag proteins to co-opt cellular budding pathways for release.

PMEL is a pigment cell-specific protein that forms a functional amyloid matrix in melanosomes. The matrix consists of well-separated fibrillar sheets on which the pigment melanin is deposited. Using electron tomography, we demonstrate that this sheet architecture is governed by the PMEL repeat (RPT) domain, which associates with the amyloid as an accessory proteolytic fragment. Thus, the RPT domain is dispensable for amyloid formation as such but shapes the morphology of the matrix, probably in order to maximize the surface area available for pigment adsorption. Although the primary amino acid sequence of the RPT domain differs vastly among various vertebrates, we show that it is a functionally conserved, interchangeable module. RPT domains of all species are predicted to be very highly O-glycosylated, which is likely the common defining feature of this domain. O-glycosylation is indeed essential for RPT domain function and the establishment of the PMEL sheet architecture. Thus, O-glycosylation, not amino acid sequence, appears to be the major factor governing the characteristic PMEL amyloid morphology.

Although relatively small in size, the ZZ-type zinc finger (ZZ) domain is a versatile signaling module that is implicated in a diverse set of cell signaling events. Here, we highlight the most recent studies focused on the ZZ domain function as a histone reader and a sensor of protein degradation signals. We review and compare the molecular and structural mechanisms underlying targeting the amino-terminal sequences of histone H3 and arginylated substrates by the ZZ domain. We also discuss the ZZ domain sensitivity to histone PTMs and summarize biological outcomes associated with the recognition of histone and non-histone ligands by the ZZ domain-containing proteins and complexes.

The automotive megatrends (electrification, automation, connectivity) and new mobility concepts lead to an increasing interaction of mechatronic systems with their surrounding systems and finally to an increased interaction with the entire vehicle. This leads to changed boundary conditions for OEMs and Tier1 suppliers.