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The set contains 200 images of various wooden bricks of various shapes and colors placed on a background (blanket) with some heart shaped patterns. Each photo is available in 300x300 and 224x224 pixels size in PNG format. Photos are divided in 10 classes – 8 types of bricks photographed form various angles + 2 additional classes (multiple bricks at one photo; empty background).

Frequency Response Functions (FRF) obtained for Sandvik CoroBore® 825 XL mounted at WHN 13-15 TOS VARNSDORF CNC machine at the minimum extension of the spindle adaptor. Tool set to bore a hole with a diameter 733mm

Przedkładany Czytelnikowi podręcznik w jakiejś mierze stanowi odzwierciedlenie wykładów z przedmiotu analiza matematyczna 2 dla studentów pierwszego stopnia matematyki stosowanej. Notatki do wykładów istniały już wcześniej w różnej postaci i postanowiłem je połączyć w pewną całość. Mam świadomość, iż wprowadzane przeze mnie podejście nie jest w żadnej mierze nowatorskie, ale tak zredagowany podręcznik może być przydatny dla studentów Politechniki Łódzkiej.

The paper presents the theoretical background and four applications examples of the new method for the estimation of support stiffness coefficients of complex structures modelled discretely (e.g. with the use of the Finite Element Model (FEM) method based on the modified Particle Swarm Optimization (PSO) algorithm. In real-life cases, exact values of the supports’ stiffness coefficients may change for various reasons (e.g. order of fastening, state of the contact surfaces, environment changes, etc.). Because of the unknown coefficients, reliable simulations of fixed structure (i.e. mounted, assembled, not in a free-free state) are difficult to perform. The method serves as a tool to obtain good correlation between the FEM of a structure and the experimental data. Simple modal tests are required to estimate the first few modes of the fixed system. The FEM of the structure is considered in a free-free state and the support stiffness coefficients of the FEM are estimated by the proposed method. Further simulations with test-tuned and correlated complete FEM could be performed in time or frequency domain.

In this note we consider the classical variational tools like: Ekelenad's Variational Principle, Mountain Pass Lemma and some of their corollaries subject to a parameter. Next, we investigate the behaviour of critical points obtained once a sequence of parameters is allowed to be convergent. Applications for the Dirichlet Boundary Value Problem on the Sierpi\'{n}ski Gasket are given in presence of assumptions which lead to fulfillment of the mountain geometry.

In this note we consider the classical variational tools like: Ekelenad's Variational Principle, Mountain Pass Lemma and some of their corollaries subject to a parameter. Next, we investigate the behaviour of critical points obtained once a sequence of parameters is allowed to be convergent. Applications for the Dirichlet Boundary Value Problem on the Sierpi��ski Gasket are given in presence of assumptions which lead to fulfillment of the mountain geometry.

We provide sufficient conditions for a mapping ƒ: Rn → Rn to be a global diffeomorphism in case ƒ need not be continuously differentiable. Instead it is assumed to be strictly (Hadamard-like) and Frechet differentiable. We use classical local invertibility conditions together with the non-smooth critical point theory.Mathematics Subject Classication (2010): 57R50, 58E05.Key words: Global diffeomorphism, local diffeomorphism, inverse function, mountain pass lemma, non-smooth critical point theory.

We use the direct variational method, the Ekeland variational principle, the mountain pass geometry and Karush-Kuhn-Tucker theorem in order to investigate existence and multiplicity results for boundary value problems connected with the discrete p(.)-Laplacian on weighted finite graphs. Several auxiliary inequalities for the discrete p(.)-Laplacian on finite graphs are also derived. Positive solutions are considered.

We provide sufficient conditions for a mapping $f:R^{n}\rightarrow R^{n}$ to be a global diffeomorphism in case it is strictly (Hadamard) differentiable. We use classical local invertibility conditions together with the non-smooth critical point theory.

In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function a , a nonlinear term f, and a numerical parameter l :D (a (k) |D u(k-1)|p(k-1)-2D u(k-1)) + l f(k,u(k))=0, k\in [1,T] . We derive the intervals of a numerical parameter l for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived.

In this note a critical point result for differentiable functionals is exploited in order to prove that a suitable class of one-dimensional fractional problems admits at least one non-trivial solution under an asymptotical behaviour of the nonlinear datum at zero. A concrete example of an application is then presented.

We provide sufficient conditions for a mapping acting between two Banach spaces to be a diffeomorphism., Comment: submitted to a journal for consideration

Using mountain pass arguments and the Karsuh-Kuhn-Tucker Theorem, we prove the existence of at least two positive solution of the anisotropic discrete Dirichlet boundary value problem. Our results generalize and improve those of [15]., preprint submitted for publication

Using the direct method of the calculus of variations we investigate the existence, uniqueness and continuous dependence on parameters for solutions of second order discrete anisotropic equations with Dirichlet boundary conditions., Comment: paper is accepted by Journal of Difference Equations and Applications, no. GDEA-2012-0047

Using min-max inequality we investigate the existence of solutions and thier dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the Euler action functional., This preprint has been submitted for publication

Using critical point theory methods we undertake the existence and multiplicity of solutions for discrete anisotropic two-point boundary value problems., preprint submitted to Elsevier

We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden-Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigation the dependence on paramaters of discrete boundary value problems., Comment: This preprint has been submitted for publication

We investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications for discrete Emden-Fowler equation are also given., Comment: The final version of this submission has been accepted for publication and it will be published in Journal of Difference Equations and Applications

We prove the existence of a strong solution of a periodic-Dirichlet problem for the semilinear wave equation with irrational period and with nonlinearity satisfying some general growth conditions locally around $0$. We construct a new variational method, called a dual method, and using relations between critical points and critical values of the primal action and the dual action functionals we prove that the solution exists. The dual functional which we define is different from the ones known so far in that it depends on two dual variables.

We show the existence and stability of solutions for a family of Dirichlet problems−div(a(x)|∇u(x)|p(x)−2∇u(x))+b(x)|u(x)|p(x)−2u(x)=Fuk(x,u(x)),u(x)|∂Ω=0,u∈W01,p(x)(Ω) with nonlinearity satisfying some local growth conditions. We construct a new duality theory which differs from the known ones in that it does not require a type of a Palais–Smale condition.