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In this paper, we introduce some explicit and recursive formulas for the n$$ n $$th q$$ q $$‐derivative of a quotient of two functions. We establish the connections between linear algebra, the homomorphisms between commutative algebras and the properties of q$$ q $$‐differential operator. One of the formulas involves the determinant of the functions and their q$$ q $$‐derivatives. Then, we show that the formulas in the classical mathematical analysis are their special cases. Finally, we used formulas to obtain some interesting q$$ q $$‐identities. [ABSTRACT FROM AUTHOR]

We study the star and minus partial orders on the set $ {\mathcal {B}}(H,K) $ B (H , K) of all bounded operators acting from a Hilbert space H to a Hilbert space K. We extend and strengthen some results from matrix case to the case of general operators, which may not possess generalized inverses. By means of some norm inequalities, we give necessary and sufficient condition under which two operators have orthogonal ranges, and thus, we give a characterization of the star partial order. When A = PB for some projection P, we prove the equivalence of $ A \lt ^*B $ A < ∗ B with $ f(AA^*)A \lt ^*f(BB^*)B $ f (A A ∗) A < ∗ f (B B ∗) B for a wide class of continuous functions f. Also, we prove that $ A \lt ^*B $ A < ∗ B if and only if $ A \lt ^-B $ A < − B and $ A^2 \lt ^{-}B^{2} $ A 2 < − B 2 when A is a weak EP operator and B is a self-adjoint operator. Finally, we consider the Moore–Penrose invertibility and the ordinary invertibility of a linear combination of operators when they are related with one of these two orders. [ABSTRACT FROM AUTHOR]

The paper presents the procedure for determining the factor of safety (FoS) using the strength reduction method (SRM) for the case of a concrete damage plasticity constitutive model. The SRM was originally used in a slope stability analysis and in its original form, this method was applied by reducing the shear strength of the material. Since damage in concrete occurs due to exceeding the normal stresses in the principal directions, and not due to exceeding the shear strength, this method was modified and adapted to the concrete damage plasticity constitutive model. Instead of reducing the failure surface, the parameters which describe the mechanical behavior in the case of uniaxial compression and uniaxial tension were reduced. In this way, the reduction of stress and the corresponding strain was carried out in the entire range of total strain, without changing the shape of the failure surface in the deviator plane. For the proposed methodology, a numerical algorithm was developed and implemented into the software PAK. The algorithm was verified through test examples and the obtained results were compared with analytically calculated FoS. The excellent agreement is observed between the FoS obtained by applying the proposed algorithm and the analytically calculated FoS. [ABSTRACT FROM AUTHOR]

This paper presents a method for implicit stress integration of the Drucker-Prager material model with kinematic hardening. The stress integration of the material model is conducted using the incremental plasticity method, while the kinematic hardening of material is defined using nonlinear Armstrong-Frederick hardening. This type of granular material hardening occurs as a consequence of the cyclic loading effects, such as the seismic load. For this reason, this material model is used for the earthquake analysis in the soil mechanics. Yield surface of the material model changes its position under the cyclic loads in the stress space, whereas there is no change in the size of the yield surface in deviatoric plane. The developed algorithm of the material model has been implemented in the software package PAK. [Projekat Ministarstva nauke Republike Srbije, br. TR37013 i br. TR32036]

A positive answer on a question posed in Eshkaftaki et al. [DSS-weak majorization and its linear preservers on ℓ p spaces. Linear Multilinear Algebra. 2018;66(10):2076–2088] is provided. Precisely, the concrete form of bounded linear operators which preserve DSS-weak majorization on discrete Lebesgue space ℓ 1 (I) , when I is an infinite set, is presented. Interestingly, it is shown that the class of DSS-weak majorization preservers is a proper subset of the class of majorization preservers on ℓ 1 (I) , despite the fact that these two classes of preservers coincide [Eshkaftaki et al. DSS-weak majorization and its linear preservers on ℓ p spaces. Linear Multilinear Algebra. 2018;66(10):2076–2088] when above relations are defined on ℓ p (I) when p ∈ (1 , ∞). In this way, the conjecture given at the end of the paper [Eshkaftaki et al. DSS-weak majorization and its linear preservers on ℓ p spaces. Linear Multilinear Algebra. 2018;66(10):2076–2088] is confirmed. [ABSTRACT FROM AUTHOR]

The procedure for identifying concrete damage plasticity material model parameters is presented in this paper. Concrete damage plasticity material model represents a constitutive model which is based on a combination of theory of plasticity and theory of damage mechanics. This material model is often used in solving geotechnical problems due to its realistic description of mechanical behavior of concrete material. Theoretical basis of concrete damage plasticity material model and material parameters identification procedure are presented in this paper. Proposed identification procedure is applied on experimental data from uniaxial compression and tension load-unload tests taken from literature. By applying experimental data, stress-strain curve is created. Based on stress-strain load-unload curve, stress-plastic strain and stress-degradation dependences are created which are necessary for material parameters identification. Using these dependences material parameters are determined. Verification of estimated parameters is performed in PAK software package using concrete damage plasticity material model. Finite element model is created for numerical simulations of uniaxial compression and tension tests. Numerical simulation results are compared with experimental data. By comparing numerical simulation results and experimental data it can be concluded that this procedure is effective for determining concrete damage plasticity model parameters. [ABSTRACT FROM AUTHOR]

A stress-strain history in the material of real concrete structures is usually unknown. An effect of concrete degradation is analyzed to describe how the initial degradation parameter can describe the stress-strain history. The idea is to introduce the initial damage of the structure by the degradation parameter to calculate the internal variables of the constitutive model. Six numerical examples are proposed to verify the methodology for various loading conditions. Based on the obtained results, it was shown that unknown stress-strain history could be successfully represented using the original material parameters and the initial degradation of the concrete. The stress-strain behavior of the damaged concrete is successfully simulated and essential for the structural analysis of civil engineering structures. [ABSTRACT FROM AUTHOR]

Letbe a unital ring admitting involution. We introduce an order onand show that in the case whenis a Rickart-ring, this order is equivalent to the well-known star partial order. The notion of the left-star and the right-star partial orders is extended to Rickart-rings. Properties of the star, the left-star and the right-star partial orders are studied in Rickart-rings and some known results are generalized. We found matrix forms of elementsandwhen, whereis one of these orders. Conditions under which these orders are equivalent to the minus partial order are obtained. The diamond partial order is also investigated. [ABSTRACT FROM AUTHOR]

This paper is the result of research and operation modeling of the new systems for cooling of cutting tools based on thermoelectric module. A copper inlay with thermoelectric module on the back side was added to a standard turning tool for metal processing. For modeling and simulating the operation of thermoelectric module, finite element method was used as a method for successful solving the problems of inhomogeneous transient temperature field on the cutting tip of lathe knives. Developed mathematical model is implemented in the software package PAK-T through which numerical results are obtained. Experimental research was done in different conditions of thermoelectric module operation. Cooling of the hot module side was done by a heat exchanger based on fluid using automatic temperature regulator. After the calculation is done, numerical results are in good agreement with experimental. It can be concluded that developed mathe-matical model can be used successfully for modeling of cooling of cutting tools. [ABSTRACT FROM AUTHOR]

The paper represents a solution example of a specific engineering problem using thermo-mechanical analysis. The paper provides theoretical basis of numerical solving the problem of heat conducting through continuum using the finite element method. Calculation of heat conducting using the finite element method determines the temperature field used as an input for thermo-mechanical calculation. The basic task of thermo-mechanical calculation was the identification of the cause of cracks on the powder material transport wagon. After the analysis of the wagon crack causes, repair of the cracks is suggested. Repeating of the FEM analysis on the reconstructed model confirms that the wagon satisfies the criteria of static and fatigue strength appointed by the standards. [ABSTRACT FROM AUTHOR]