Issue 3
JTAM, Sofia, vol. 56 Issue 3 (2026)

LOCAL SOLVABILITY OF THE PARABOLIC POINCARÉ PROBLEM WITH EMERGENT TYPE VECTOR FIELD

Dian K. Palagachev1, Lubomira G. Softova2, Salvatore Tramontano2
1Department of Mechanics, Mathematics and Management, Polytechnic University of Bari, Italy
2Department of Mathematics, University of Salerno, Italy


We prove local strong solvability of the oblique derivative problem for linear second-order parabolic equations in the case when the vector field, defining the boundary operator, can be tangent to the boundary and is of emergent type. A~priori estimates in suitable Sobolev spaces are derived for the solution as well.

doi: https://doi.org/10.55787/jtams.2026.3.AI00319

JTAM, Sofia, vol. 56 Issue 3 pp. 267-282 (2026), [Full Article]

ANALYTICAL CONSTRUCTION OF THE SCHRÖDINGER--NEWTON GROUND STATE VIA THE HOMOTOPY ANALYSIS METHOD WITH VIRIAL CALIBRATION

George Venkov, Petia Zorovska
Department of Mathematical Analysis and Differential Equations, Technical University of Sofia, Kliment Ohridski Blvd. 8, 1000 Sofia, Bulgaria

We present an analytical approximation of the spherically symmetric ground state of the Schrödinger--Newton system using the Homotopy Analysis Method. The construction rests on an inner expansion in an exponential basis, regular at the origin and with the correct exponential decay. We recover the non-integer Coulomb prefactor of the far-field decay, which lies outside the basis, by an envelope factorisation of the radial equation. We compute the first-order correction, fix the physical amplitude at each truncation by the virial identity, select the convergence-control parameter by minimizing the residual of the amplitude-corrected field, and assemble a uniformly valid composite approximation. The corrections are elementary and exact through first order; second order and higher are obtained by spectral continuation.

doi: https://doi.org/10.55787/jtams.2026.3.AI00333

JTAM, Sofia, vol. 56 Issue 3 pp. 283-298 (2026), [Full Article]

MICROLOCAL ANALYSIS, TIME-FREQUENCY TRANSFORMS AND LOCAL UNCERTAINTY PRINCIPLES

Alessandro Oliaro
Dipartimento di Matematica, Università di Torino, Via Carlo Alberto n. 10, I-10123 Torino, Italy

In this paper we propose an uncertainty principle of local type involving the short-time Fourier transform in the frame of ultradifferentiable spaces. The classical local uncertainty principle for the Fourier transform can be seen as a refinement of the Heisenberg inequality; the results we prove in this paper assert that the L1 content of a function f in a measurable E must be small as the measure of E is small and/or the ξ-dispersion of the short-time Fourier transform of f is small, giving then a new result related with classical Fourier analysis and time-frequency representations.

doi: https://doi.org/10.55787/jtams.2026.3.AI01046

JTAM, Sofia, vol. 56 Issue 3 pp. 299-312 (2026), [Full Article]

STUDY OF THE DYNAMICS OF THE DRIVE OF THE MACHINE UNIT OF THE SEPARATOR FOR SEPARATION OF COTTON SEEDS

R.O. Muminov1, K.T. Sherov2, D.D. Juraev3, M.M. Mussayev4, A.N. Ruzibaev1, G.B. Abdugaliyeva4
1Navoi State University of Mining and Technology, Galaba ave., 76, 210100, Navoi, Uzbekistan
2Seifullin Kazakh AgroTechnical Research University, Zhenis ave., 62, 010011, Astana, Kazakhstan
3Navoi Department of the Academy of Sciences, Galaba ave., 170, 210100, Navoi, Uzbekistan
4Abylkas Saginov Karaganda Technical University, Nazarbayev ave., 56, 100027, Karaganda, Kazakhstan

The article presents the development of an effective, resource-saving design scheme for a separator, based on the analysis of existing separator designs used for separating cotton seeds. Theoretical studies have determined the influence of the rigidity of elastic elements on the impact vibrations of the shovel and have developed dynamic and mathematical models for the interaction of the machine units of the separator. Based on the numerical solution, the parameters of the working drum – such as torque and the laws of motion of angular velocities – along with the impact blade shafts and belt transmission under various technological resistances, are theoretically determined and substantiated. The laws governing the change in torque and angular velocities of the working drum are also determined. Additionally, the vibration characteristics of the impact blades are obtained, and recommended parameter values are selected based on the analysis of graphical dependencies, with a comparison between experimental results and theoretical studies.

doi: https://doi.org/10.55787/jtams.2026.3.AI00042

JTAM, Sofia, vol. 56 Issue 3 pp. 313-324 (2026), [Full Article]

SYNTHESIS OF SLIDER-CRANK MECHANISMS WITH APPLICATION OF THE THEORY OF STATIONARY CURVATURE

Blagoyka Paleva-Kadiyska1, Iliya Andonov1, Roumen Roussev2, Vitan Galabov3
1Todor Kableshkov University of Transport, Sofia, Bulgaria
2Faculty of Technics and Technology - Yambol of Trakia University, Bulgaria
3Technical University-Sofia, Bulgaria

A linear mathematical model that applies the cubic of stationary curvature theory and, in particular, the Carter-Hall's circle to generate Burmester's curves is adapted and further development for the synthesis of grippers with crank-fork mechanisms. The model also includes a condition for achieving a certain value of the pressure angle is considered, in which the kinematic diagram of the mechanism is unambiguously determined. The application of the mathematical model is illustrated by the synthesis of mechanisms of two grippers with practical application. The introduced linear mathematical model enables automated computer synthesis by four infinitely close relative positions of slider-crank mechanisms, which was considered impossible for decades. The proposed new model significantly facilitates the work of engineers in the synthesis of slider-crank mechanisms, which are very often found in modern devices such as e.g. some grippers for robots in microelectronics. The new method avoids the shortcoming of the known methods of synthesis by infinitely close positions, namely the non-linear mathematical models for synthesis that are reached with them. The developed linear model is easy to implement with any computer program for engineering calculations (eg. MathCAD, Mathlab, etc.).

doi: https://doi.org/10.55787/jtams.2026.3.AI00139

JTAM, Sofia, vol. 56 Issue 3 pp. 325-334 (2026), [Full Article]

FREE VIBRATION OF BIO-INSPIRED HELICOIDAL COMPOSITE BEAMS WITH EXPONENTIALLY GRADED LAYERS

Bathini Sidda Reddy1, K. Vijaya Kumar Reddy2, B. Chinna Ankanna1
1Department of Mechanical Engineering, Rajeev Gandhi Memorial College of Engineering & Technology, Nandyal-518501, India
2Department of Mechanical Engineering, Jawaharlal Nehru Technological University, Hyderabad, India

This paper presents the free vibration behaviour of bio-inspired helicoidally symmetric laminated composite (BIHSLC) beams using higher-order shear deformation theory (HSDT) via the Ritz method. The stiffness and mass matrices are formulated through a variational approach, and the governing equations of motion are derived accordingly. The developed model is validated against existing results. A comprehensive study is conducted to investigate the influence of lamination schemes, number of layers, boundary conditions, grading parameters, aspect ratios, and orthotropy ratios. Notably, the fundamental frequencies exhibit significant variation depending on the specific lamination scheme, boundary conditions, grading parameters, number of layers, and aspect ratio. The novel insights presented in this study contribute to the understanding and future design of advanced composite beam structures.

doi: https://doi.org/10.55787/jtams.2026.3.AI00201

JTAM, Sofia, vol. 56 Issue 3 pp. 335-353 (2026), [Full Article]

APPLICATION OF ARTIFICIAL INTELLIGENCE TO CONTROL AND PREDICT THE QUALITY OF ASPHALT CONCRETE COATING

Yaroslav Steshenko1, Anatolii Protasov1, Yurii Kuts1, Iuliia Lysenko1,2, Yordan Mirchev2,3
1National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute'', Kyiv, Ukraine
2Center of Competence for Mechatronics and Clean Technologies "Mechatronics, Innovation, Robotics, Automation and Clean Technologies'' - MIRACle, Bulgaria
3Institute of Mechanics at the Bulgarian Academy of Sciences, Sofia, Bulgaria

The article is devoted to the problems of controlling and predicting the quality of asphalt concrete pavement at the laying stage using artificial intelligence methods. An intelligent system is proposed that uses a neural network model to analyze key process parameters-temperature, humidity, compaction pressure, and placement speed-to identify potentially defective areas. The developed system allows you to identify areas with a risk of under compaction even during laying, which allows the operator to timely adjust the technological parameters of the process. As a result, the implemented system achieved a prediction accuracy of 96%, which significantly improves the efficiency of real-time coating.

doi: https://doi.org/10.55787/jtams.2026.3.AI00263

JTAM, Sofia, vol. 56 Issue 3 pp. 354-372 (2026), [Full Article]

MATHEMATICAL ANALYSIS OF A DIMENSIONALLY REDUCED VISCOELASTIC PROBLEM WITH LOGARITHMIC SOURCE AND NONLINEAR FRICTION

Mohamed Dilmi1, Mourad Dilmi2
1LAMDA-RO Laboratory, Department of Mathematics, University of Blida 1, Po. Box 270 Soumaa, Blida, Algeria
2Laboratory for Applied Mathematics, Department of Mathematics, Setif I-University, 19000, Algeria

This paper studies the dimensional reduction of a nonlinear viscoelastic problem posed in a thin domain 𝒟ξ ⊂ ℝ3, featuring a logarithmic source term and mixed boundary conditions. The model combines a Dirichlet boundary condition on one portion of the boundary with non-linear slip conditions described by a Tresca friction law on the remaining parts. Using asymptotic analysis, we rigorously derive the limiting behavior of the solution as the thickness parameter ξ approaches zero. Our results show that the three-dimensional solution converges to a well-defined two-dimensional limit problem, where the effects of the Tresca friction are preserved in the reduced formulation. Additionally, we prove the uniqueness of the solution to the limiting problem, ensuring the well-posedness of the derived model.

doi: https://doi.org/10.55787/jtams.2026.3.AI00264

JTAM, Sofia, vol. 56 Issue 3 pp. 373-397 (2026), [Full Article]

APPLICATION OF THE HILBERT METHOD TO FREE-SURFACE FLOW PROBLEMS

Bochra Amroune, Abdelkader Gasmi
Laboratory of Pure and Applied Mathematics, Faculty of Mathematics and Informatics, University of M’sila, Algeria

This paper investigates the two-dimensional flow of a free surface of an inviscid and incompressible fluid over a non-smooth bottom. It considers the surface tension effect while neglecting gravity. The potential region in the W-plane is transformed onto the auxiliary λ-plane using the Schwarz-Christoffel transformation. The primary goal of this study is to offer an approximate solution to this problem employing the perturbation approach and the Hilbert transformation. The computations are conducted for high Weber numbers and small slopes of the bottom. Solutions are presented and illustrated up to the first-order approximation. Free-surface shapes for various Weber numbers and different small slopes are plotted.

doi: https://doi.org/10.55787/jtams.2026.3.AI00266

JTAM, Sofia, vol. 56 Issue 3 pp. 398-411 (2026), [Full Article]