Real vector spaces

Part 2 of ebook "Linear algebra done right (Third edition)" provides readers with contents including: Chapter 6 - Inner product spaces; Chapter 7 - Operators on inner product spaces; Chapter 8 - Operators on complex vector spaces; Chapter 9 - Operators on real vector spaces; Chapter 10 - Trace and determinant;...

175p daonhiennhien 03-07-2024 2 1   Download

Part 1 of ebook "Measure, integration and real analysis" provides readers with contents including: chapter 1 - Riemann integration; chapter 2 - Measures; chapter 3 - Integration; chapter 4 - Differentiation; chapter 5 - Product measures; chapter 6 - Banach spaces;...

211p tieulangtran 28-09-2023 8 2   Download

Part 1 of ebook "Applied linear algebra (Second edition)" has presents the following content: Chapter 1 - Linear algebraic systems; Chapter 2 - Vector spaces and bases; Chapter 3 - Inner products and norms; Chapter 4 - Orthogonality; Chapter 5 - Minimization and least squares;...

325p dieptieuung 20-07-2023 7 3   Download

In this paper, we study the systems of generalized multivalued strong vector quasi-equilibrium problem (in short (SQVEP)) real locally convex Hausdorff topological vector spaces. This problem includes as special cases the generalized strong vector quasi-equilibrium problems, quasi-equilibrium problems, equilibrium problems and variational inequality problems.

4p vilexus 30-09-2022 4 2   Download

In this paper, we establish existence results of fixed point for mixed monotone operators in a real Hausdorff locally convex topological vector space without normality of cone. Our result is an extension of Z. Zhang- K. Wang.

7p viirenerosenfeld 02-06-2022 12 1   Download

A sequence of negatively superadditive dependent random vectors taking values in a real separable Hilbert space. This paper presents some results on weak laws of large numbers for weighted sums (with or without random indices).

9p meyerowitz 25-12-2021 5 0   Download

In this paper we propose results on zero duality gap in vector optimization problems posed in a real locally convex Hausdorff topological vector space with a vector-valued objective function to be minimized under a set and a convex cone constraint. These results are then applied to linear programming.

14p nguaconbaynhay12 03-06-2021 13 1   Download

In this paper, we establish some existence theorems by using Kakutani-FanGlicksberg fixed-point theorem for generalized quasiequilibrium problems in real locally convex Hausdorff topological vector spaces. Moreover, we also discuss closeness of the solution sets of generalized quasiequilibrium problems. The results presented in the paper improve and extend the main results of Long et al in [3], Plubtieng - Sitthithakerngkietet in [5] and Yang-Pu in [6].

7p nguaconbaynhay 20-10-2019 11 1   Download

Following the study on volume of indicatrices in a real Finsler space, in this paper we are investigating some volume properties of the indicatrix considered in an arbitrary fixed point of a complex Finsler manifold. Since for each point of a complex Finsler space the indicatrix is an embedded CR-hypersurface of the punctured holomorphic tangent bundle, by means of its normal vector, the volume element of the indicatrix is determined.

15p danhdanh27 07-01-2019 16 2   Download

In this paper, we study the basic results on the general study of null curves in the Minkowski 4-space R4 1. A transversal vector bundle of a null curve in R4 1 is constructed using a frenet Frame consisting of two real null and two space-like vectors. The null curves are characterized by using the Frenet frame.

8p danhdanh27 07-01-2019 19 1   Download

In this paper, we establish some existence theorems for vector quasiequilibrium problems in real locally convex Hausdorff topological vector spaces by using Kakutani-Fan-Glicksberg fixedpoint theorem. Moreover, we also discuss the closedness of the solution sets for these problems. The results presented in the paper are new and improve some main results in the literature.

10p danhvi10 22-11-2018 27 0   Download

There are notes of course of lectures on Field theory aimed at providing the beginner with an introduction to algebraic extensions, algebraic function fields, formally real fields and valuated fields. These lectures were preceded by an elementary course on group theory, vector spaces and ideal theory of rings—especially of Noetherian rings. A knowledge of these is presupposed in these notes.

0p nunongnuna 01-04-2013 72 15   Download

The Fourier transform of a C ∞ function, f , with compact support on a real reductive Lie group G is given by a collection of operators φ(P, σ, λ) := π P (σ, λ)(f ) for a suitable family of representations of G, which depends on a family, indexed by P in a finite set of parabolic subgroups of G, of pairs of parameters (σ, λ), σ varying in a set of discrete series, λ lying in a complex finite dimensional vector space. The π P (σ, λ) are generalized principal series, induced from P . It is...

44p noel_noel 17-01-2013 58 5   Download

Hilbert Spaces 1.1 Inner product spaces Example 1.1 Prove that in a real vector space with inner product we have (x, y) = 1 4 x + y2 − x − y2, and in a complex vector space with inner product we have (x, y) = 1 4 x + y2 − x − y2 + i x + iy2 + i x − iy2. These are the so-called polarization identities. They tell us that in a Hilbert space, the inner product is determined by the norm.

109p sn_buon 29-11-2012 51 4   Download

The purpose of this volume is to present some worked out examples from the theory of Functions in Several Variables in the following topics: 1) Maximum and minimum of a function. 2) Integration in the plane and in the space. 3) Vector analysis. As an experiment I shall here use the following generic diagram for solving problems:

91p sn_buon 29-11-2012 55 2   Download

The purpose of this volume is to present some worked out examples from the theory of Functions in Several Variables in the following topics: 1) Maximum and minimum of a function. 2) Integration in the plane and in the space. 3) Vector analysis. As an experiment I shall here use the following generic diagram for solving problems: A. For Awareness. What is the problem? Try to formulate the problem in your own words, thereby identifying it. D. For Decision. What are we going to do with it? Are there any reasonable solution procedure available? If so, which one should be chosen?...

0p sn_buon 29-11-2012 64 0   Download

A Class of Normalised Algorithms for Online Training of Recurrent Neural Networks A normalised version of the real-time recurrent learning (RTRL) algorithm is introduced. This has been achieved via local linearisation of the RTRL around the current point in the state space of the network. Such an algorithm provides an adaptive learning rate normalised by the L2 norm of the gradient vector at the output neuron. The analysis is general and also covers simpler cases of feedforward networks and linear FIR filters...

12p doroxon 12-08-2010 89 15   Download

Decoupled flux and torque control of an induction machine can be realised by control of instantaneous phase current values, which in turn can be achieved by stator current space vector magnitude and position control with respect to the chosen flux space vector. As already discussed in the Section 2.3.3., a vector is composed of appropriate d-q axis components, d-axis component being the real part and qaxis component being the imaginary part of the vector (i.e. d-q axes are mutually perpendicular, as already emphasised). ...

10p liemthanh 15-12-2009 66 7   Download