Matrix methods for perfect signal recovery underlying range space of operators

The purpose of this work is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by a new matrix method. To this end, first we obtain more structures of the canonical $K$-dual. % and survey optimal $K$-dual problem under probabilistic erasures. Then, we survey the problem of recovering and robustness of signals when the erasure set satisfies the minimal redundancy condition or the $K$-frame is maximal robust. Furthermore, we show that the error rate is reduced under erasures if the $K$-frame is of uniform excess. Toward the protection of encoding frame (K-dual) against erasures, we introduce a new concept so called $(r,k)$-matrix to recover lost data and solve the perfect recovery problem via matrix equations. Moreover, we discuss the existence of such matrices by using minimal redundancy condition on decoding frames for operators. We exhibit several examples that illustrate the advantage of using the new matrix method with respect to the previous approaches in existence construction. And finally, we provide the numerical results to confirm the main results in the case noise-free and test sensitivity of the method with respect to noise.

Pietsch’s variants of s-numbers for multilinear operators

We study variants of s-numbers in the context of multilinear operators. The notion of an $$s^{(k)}$$ s ( k ) -scale of k-linear operators is defined. In particular, we shall deal with multilinear variants of the $$s^{(k)}$$ s ( k ) -scales of the approximation, Gelfand, Hilbert, Kolmogorov and Weyl numbers. We investigate whether the fundamental properties of important s-numbers of linear operators are inherited to the multilinear case. We prove relationships among some $$s^{(k)}$$ s ( k ) -numbers of k-linear operators with their corresponding classical Pietsch’s s-numbers of a generalized Banach dual operator, from the Banach dual of the range space to the space of k-linear forms, on the product of the domain spaces of a given k-linear operator.

NDSHA - The New Paradigm for RSHA - An Updated Review

A New Paradigm (data driven and not like the currently model driven) is needed for Reliable Seismic Hazard Assessment RSHA. Neo-Deterministic Seismic Hazard Assessment (NDSHA) integrates earthquake geology, earthquake science, and particularly earthquake physics to finally achieve a New (and needed) Paradigm for Reliable Seismic Hazard Assessment RSHA.Although observations from many recent destructive earthquakes have all confirmed the validity of NDSHA’s approach and application to earthquake hazard forecasting-nonetheless damaging earthquakes still cannot yet be predicted with a precision requirement consistent with issuing a red alert and evacuation order to protect civil populations. However, intermediate-term (time scale) and middle-range (space scale) predictions of main shocks above a pre-assigned threshold may be properly used for the implementation of low-key preventive safety actions, as recommended by UNESCO in 1997. Furthermore, a proper integration of both seismological and geodetic information has been shown to also reliably contribute to a reduction of the geographic extent of alarms and it therefore defines a New Paradigm for TimeDependent Hazard Scenarios: Intermediate-Term (time scale) and Narrow-Range (space scale) Earthquake Prediction.

NDSHA - The New Paradigm for RSHA - An Updated Review

A New Paradigm (data driven and not like the currently model driven) is needed for Reliable Seismic Hazard Assessment RSHA. Neo-Deterministic Seismic Hazard Assessment (NDSHA) integrates earthquake geology, earthquake science, and particularly earthquake physics to finally achieve a New (and needed) Paradigm for Reliable Seismic Hazard Assessment RSHA.Although observations from many recent destructive earthquakes have all confirmed the validity of NDSHA’s approach and application to earthquake hazard forecasting-nonetheless damaging earthquakes still cannot yet be predicted with a precision requirement consistent with issuing a red alert and evacuation order to protect civil populations. However, intermediate-term (time scale) and middle-range (space scale) predictions of main shocks above a pre-assigned threshold may be properly used for the implementation of low-key preventive safety actions, as recommended by UNESCO in 1997. Furthermore, a proper integration of both seismological and geodetic information has been shown to also reliably contribute to a reduction of the geographic extent of alarms and it therefore defines a New Paradigm for TimeDependent Hazard Scenarios: Intermediate-Term (time scale) and Narrow-Range (space scale) Earthquake Prediction.

Karamardian Matrices: An Analogue of Q-Matrices

A real square matrix $A$ is called a $Q$-matrix if the linear complementarity problem LCP$(A,q)$ has a solution for all $q \in \mathbb{R}^n$. This means that for every vector $q$ there exists a vector $x$ such that $x \geq 0, y=Ax+q\geq 0$, and $x^Ty=0$. A well-known result of Karamardian states that if the problems LCP$(A,0)$ and LCP$(A,d)$ for some $d\in \mathbb{R}^n, d >0$ have only the zero solution, then $A$ is a $Q$-matrix. Upon relaxing the requirement on the vectors $d$ and $y$ so that the vector $y$ belongs to the translation of the nonnegative orthant by the null space of $A^T$, $d$ belongs to its interior, and imposing the additional condition on the solution vector $x$ to be in the intersection of the range space of $A$ with the nonnegative orthant, in the two problems as above, the authors introduce a new class of matrices called Karamardian matrices, wherein these two modified problems have only zero as a solution. In this article, a systematic treatment of these matrices is undertaken. Among other things, it is shown how Karamardian matrices have properties that are analogous to those of $Q$-matrices. A subclass of a recently introduced notion of $P_{\#}$-matrices is shown to possess the Karamardian property, and for this reason we undertake a thorough study of $P_{\#}$-matrices and make some fundamental contributions.

Modeling and Simulation of Departure Passenger’s Behavior Based on an Improved Social Force Approach: A Case Study on an Airport Terminal in China

The unprecedented growth of passenger throughput in large airport terminals highlights the importance of analyzing passengers’ movement to achieve airport terminal’s elaborate management. Based on the theory of original social force model, video data from a departure hall of a large airport terminal in China were analyzed to summarize passengers’ path planning characteristics. Then, a double-level model was established to describe passengers’ path planning behaviors. At the decision level of the proposed model, the avoiding force model including common avoiding force and additional horizontal avoiding force was established on the basis of setting time and space limitations for taking avoiding action and was used to describe passengers’ path planning in close-range space. At the tactical level of the proposed model, the route and node choice models were established to describe passengers’ path planning in long-range space. In the route choice model, a distribution of intermediate destination areas was proposed, with detouring distance, pedestrian density, speed difference, and pedestrian distribution considered in choosing an intermediate destination area. In the node choice model, the walking distance, the quantity of people waiting, and luggage were considered in choosing a check-in counter or security check channel. The main parameters of the proposed model were confirmed according to video data. Simulation results show that the proposed model can simulate departure passengers’ path planning behaviors at an acceptable accuracy level.

Further characterizations of the weak core inverse of matrices and the weak core matrix

<abstract><p>The present paper is devoted to characterizing the weak core inverse and the weak core matrix using the core-EP decomposition. Some new characterizations of the weak core inverse are presented by using its range space, null space and matrix equations. Additionally, we give several new representations and properties of the weak core inverse. Finally, we consider several equivalent conditions for a matrix to be a weak core matrix.</p></abstract>

On boundedness of the Hilbert transform on Marcinkiewicz spaces

We study boundedness properties of the classical (singular) Hilbert transform (Hf)(t) = p.v.1/π \int_R f(s)/(t − s)ds acting on Marcinkiewicz spaces. The Hilbert transform is a linear operator which arises from the study of boundary values of the real and imaginary parts of analytic functions. Questions involving the H arise therefore from the utilization of complex methods in Fourier analysis, for example. In particular, the H plays the crucial role in questions of norm-convergence of Fourier series and Fourier integrals. We consider the problem of what is the least rearrangement-invariant Banach function space F(R) such that H : Mφ(R) → F(R) is bounded for a fixed Marcinkiewicz space Mφ(R). We also show the existence of optimal rearrangement-invariant Banach function range on Marcinkiewicz spaces. We shall be referring to the space F(R) as the optimal range space for the operator H restricted to the domain Mφ(R) ⊆ Λϕ0(R). Similar constructions have been studied by J.Soria and P.Tradacete for the Hardy and Hardy type operators [1]. We use their ideas to obtain analogues of their some results for the H on Marcinkiewicz spaces.

ISS - a Platform for Developing a System for Hypogravitational Disturbances Countermeasures in Interplanetary Missions

The paper contains modern understanding of gravity-dependent changes in human body systems that occur during space flight and of modern problems, the solution of which will bring humanity closer to ensuring medical safety in interplanetary missions. Particular consideration is given to the state of the systems limiting physical performance, which is a factor that largely determines the success of planetary activities in ultra-long-range space flights. Hypogravitational disturbances countermeasures used on the ISS are described, with emphasis on some features that are specific to the ISS partners. Prospects for development of countermeasures for hypogravitational disorders in interplanetary missions are considered.