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Prof. Volodymyr Sushch
Koszalin University of Technology

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0 Differential Equations
0 boundary value problems
0 discrete models
0 discrete operators
0 discrete Dirac equation

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discrete Dirac equation
discrete models
Differential Equations
boundary value problems

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Journal article
Published: 17 April 2021 in Sustainability
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The COVID pandemic has touched many aspects of everyone’s life. Education is one of the fields greatly affected by it, as students and teachers were forced to move online and quickly adapt to the online environment. Assessment is a crucial part of education, especially in STEM fields. A gap analysis was performed by expert groups in the frame of an Erasmus+ project looking at the practices of six European countries. Specialists teaching university-grade mathematics in seven European institutions were asked about their perception of gaps in the assessment of students both before (2019) and during (2021) the pandemic. This qualitative study looks at the difference in perception of such gaps after almost one year of online teaching. The analysis of their responses showed that some gaps were present before the pandemic, as well as others that are specific to it. Some gaps, such as the lack of IT infrastructure and the need to adapt materials to an online environment, have been exacerbated by the outbreak.

ACS Style

Vlad Bocanet; Ken Brown; Anne Uukkivi; Filomena Soares; Ana Lopes; Anna Cellmer; Carles Serrat; Cristina Feniser; Florina Serdean; Elena Safiulina; Gerald Kelly; Joanna Cymerman; Igor Kierkosz; Volodymyr Sushch; Marina Latõnina; Oksana Labanova; M. Bruguera; Chara Pantazi; M. Estela. Change in Gap Perception within Current Practices in Assessing Students Learning Mathematics. Sustainability 2021, 13, 4495 .

AMA Style

Vlad Bocanet, Ken Brown, Anne Uukkivi, Filomena Soares, Ana Lopes, Anna Cellmer, Carles Serrat, Cristina Feniser, Florina Serdean, Elena Safiulina, Gerald Kelly, Joanna Cymerman, Igor Kierkosz, Volodymyr Sushch, Marina Latõnina, Oksana Labanova, M. Bruguera, Chara Pantazi, M. Estela. Change in Gap Perception within Current Practices in Assessing Students Learning Mathematics. Sustainability. 2021; 13 (8):4495.

Chicago/Turabian Style

Vlad Bocanet; Ken Brown; Anne Uukkivi; Filomena Soares; Ana Lopes; Anna Cellmer; Carles Serrat; Cristina Feniser; Florina Serdean; Elena Safiulina; Gerald Kelly; Joanna Cymerman; Igor Kierkosz; Volodymyr Sushch; Marina Latõnina; Oksana Labanova; M. Bruguera; Chara Pantazi; M. Estela. 2021. "Change in Gap Perception within Current Practices in Assessing Students Learning Mathematics." Sustainability 13, no. 8: 4495.

Conference paper
Published: 12 March 2021 in Advances in Intelligent Systems and Computing
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The goal of this paper is to introduce a technique of creating self-tests that has allowed to actively incorporate university students into the learning process. The study was conducted within the framework of the Erasmus+ Project EngiMath. Partners’ peer reviews, the survey results and the students’ comments in forums and test results were used to conduct the research. The students’ overall satisfaction was in a high level. However, opportunities for some technical improvement has been emerged like the formulation of the tasks needs to be very clear and the time required to perform the tests must be limited. The following conclusions can be drawn from the study. The use of self-tests at all stages of training has intensified the assimilation of the material, i.e. increased understanding of theoretical material and developed computational skills. By completing a series of such assignments on each topic of the course, students had mastered the methodology of studying the topic and mastered specific teaching material on this topic. Feedback made, taking into account typical errors, has allowed the students to analyse their knowledge. A large number of variations for such tasks has allowed students to be involved in the process of active independent and individualized self-study.

ACS Style

Oksana Labanova; Elena Safiulina; Marina Latõnina; Anne Uukkivi; Vlad Bocanet; Cristina Feniser; Florina Serdean; Ana Paula Lopes; Filomena Soares; Ken Brown; Gerald Kelly; Errol Martin; Anna Cellmer; Joanna Cymerman; Volodymyr Sushch; Igor Kierkosz; Javier Bilbao; Eugenio Bravo; Olatz Garcia; Concepción Varela; Carolina Rebollar. Poster: Technique of Active Online Training: Lessons Learnt from EngiMath Project. Advances in Intelligent Systems and Computing 2021, 721 -729.

AMA Style

Oksana Labanova, Elena Safiulina, Marina Latõnina, Anne Uukkivi, Vlad Bocanet, Cristina Feniser, Florina Serdean, Ana Paula Lopes, Filomena Soares, Ken Brown, Gerald Kelly, Errol Martin, Anna Cellmer, Joanna Cymerman, Volodymyr Sushch, Igor Kierkosz, Javier Bilbao, Eugenio Bravo, Olatz Garcia, Concepción Varela, Carolina Rebollar. Poster: Technique of Active Online Training: Lessons Learnt from EngiMath Project. Advances in Intelligent Systems and Computing. 2021; ():721-729.

Chicago/Turabian Style

Oksana Labanova; Elena Safiulina; Marina Latõnina; Anne Uukkivi; Vlad Bocanet; Cristina Feniser; Florina Serdean; Ana Paula Lopes; Filomena Soares; Ken Brown; Gerald Kelly; Errol Martin; Anna Cellmer; Joanna Cymerman; Volodymyr Sushch; Igor Kierkosz; Javier Bilbao; Eugenio Bravo; Olatz Garcia; Concepción Varela; Carolina Rebollar. 2021. "Poster: Technique of Active Online Training: Lessons Learnt from EngiMath Project." Advances in Intelligent Systems and Computing , no. : 721-729.

Conference paper
Published: 21 October 2020 in Springer Texts in Business and Economics
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This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-Kähler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states for these discrete equations can be described with the aid of some projectors on a space of discrete forms. The proposed discrete model admits a chiral symmetry. We construct discrete analogues of spin operators, describe spin eigenstates for a discrete Joyce equation, and also discuss chirality (A preprint version of the article is available as ArXiv preprint: http://arxiv.org/pdf/1912.01296).

ACS Style

Volodymyr Sushch. Chiral Properties of Discrete Joyce and Hestenes Equations. Springer Texts in Business and Economics 2020, 765 -778.

AMA Style

Volodymyr Sushch. Chiral Properties of Discrete Joyce and Hestenes Equations. Springer Texts in Business and Economics. 2020; ():765-778.

Chicago/Turabian Style

Volodymyr Sushch. 2020. "Chiral Properties of Discrete Joyce and Hestenes Equations." Springer Texts in Business and Economics , no. : 765-778.

Article
Published: 30 June 2020 in Advances in Applied Clifford Algebras
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We construct a discrete version of the plane wave solution to a discrete Dirac-Kähler equation in the Joyce form. A geometric discretisation scheme based on both forward and backward difference operators is used. The conditions under which a discrete plane wave solution satisfies a discrete Joyce equation are discussed.

ACS Style

Volodymyr Sushch. A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form. Advances in Applied Clifford Algebras 2020, 30, 1 -20.

AMA Style

Volodymyr Sushch. A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form. Advances in Applied Clifford Algebras. 2020; 30 (3):1-20.

Chicago/Turabian Style

Volodymyr Sushch. 2020. "A Discrete Version of Plane Wave Solutions of the Dirac Equation in the Joyce Form." Advances in Applied Clifford Algebras 30, no. 3: 1-20.

Preprint
Published: 18 June 2019
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We construct a discrete version of the plane wave solution to a discrete Dirac-K\"{a}hler equation in the Joyce form. A geometric discretisation scheme based on both forward and backward difference operators is used. The conditions under which a discrete plane wave solution satisfies a discrete Joyce equation are discussed.

ACS Style

Volodymyr Sushch. A discrete version of plane wave solutions of the Dirac equation in the Joyce form. 2019, 1 .

AMA Style

Volodymyr Sushch. A discrete version of plane wave solutions of the Dirac equation in the Joyce form. . 2019; ():1.

Chicago/Turabian Style

Volodymyr Sushch. 2019. "A discrete version of plane wave solutions of the Dirac equation in the Joyce form." , no. : 1.

Article
Published: 05 July 2018 in Advances in Applied Clifford Algebras
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Discrete models of the Dirac–Kähler equation and the Dirac equation in the Hestenes form are discussed. A discrete version of the plane wave solutions to a discrete analogue of the Hestenes equation is established.

ACS Style

Volodymyr Sushch. A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme. Advances in Applied Clifford Algebras 2018, 28, 72 .

AMA Style

Volodymyr Sushch. A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme. Advances in Applied Clifford Algebras. 2018; 28 (4):72.

Chicago/Turabian Style

Volodymyr Sushch. 2018. "A Discrete Dirac–Kähler Equation Using a Geometric Discretisation Scheme." Advances in Applied Clifford Algebras 28, no. 4: 72.

Conference paper
Published: 08 May 2018 in Springer Texts in Business and Economics
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A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation are briefly discussed.

ACS Style

Volodymyr Sushch. Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions. Springer Texts in Business and Economics 2018, 463 -475.

AMA Style

Volodymyr Sushch. Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions. Springer Texts in Business and Economics. 2018; ():463-475.

Chicago/Turabian Style

Volodymyr Sushch. 2018. "Discrete Versions of Some Dirac Type Equations and Plane Wave Solutions." Springer Texts in Business and Economics , no. : 463-475.

Conference paper
Published: 03 September 2016 in Springer Texts in Business and Economics
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A discrete analogue of the Dirac equation in the Hestenes form is constructed by introduction of the Clifford product on the space of discrete forms. We discuss the relation between the discrete Dirac-Kähler equation and the discrete Hestenes equation.

ACS Style

Volodymyr Sushch. Discrete Dirac-Kähler and Hestenes Equations. Springer Texts in Business and Economics 2016, 433 -442.

AMA Style

Volodymyr Sushch. Discrete Dirac-Kähler and Hestenes Equations. Springer Texts in Business and Economics. 2016; ():433-442.

Chicago/Turabian Style

Volodymyr Sushch. 2016. "Discrete Dirac-Kähler and Hestenes Equations." Springer Texts in Business and Economics , no. : 433-442.

Journal article
Published: 01 October 2015 in Reports on Mathematical Physics
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We discuss a discrete analogue of the Dirac–Kähler equation in which chiral properties of the continuum counterpart are captured. We pay special attention to a discrete Hodge star operator. To build such an operator combinatorial construction of a double complex is used. We describe discrete exterior calculus operations on a double complex and obtain the discrete Dirac–Kähler equation using these tools. Self-dual and anti-self-dual discrete inhomogeneous forms are presented. The chiral invariance of the massless discrete Dirac–Kähler equation is shown. Moreover, in the massive case we prove that a discrete Dirac–Kähler operator flips the chirality.

ACS Style

Volodymyr Sushch. On the Chirality of a Discrete Dirac–Kähler Equation. Reports on Mathematical Physics 2015, 76, 179 -196.

AMA Style

Volodymyr Sushch. On the Chirality of a Discrete Dirac–Kähler Equation. Reports on Mathematical Physics. 2015; 76 (2):179-196.

Chicago/Turabian Style

Volodymyr Sushch. 2015. "On the Chirality of a Discrete Dirac–Kähler Equation." Reports on Mathematical Physics 76, no. 2: 179-196.

Journal article
Published: 01 February 2014 in Reports on Mathematical Physics
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We construct a new discrete analog of the Dirac-K\"{a}hler equation in which some key geometric aspects of the continuum counterpart are captured. We describe a discrete Dirac-K\"{a}hler equation in the intrinsic notation as a set of difference equations and prove several statements about its decomposition into difference equations of Duffin type. We study an analog of gauge transformations for the massless discrete Dirac-K\"{a}hler equations.Comment: 19 pages; added references; to appear in Rept. Math. Phy

ACS Style

Volodymyr Sushch. A discrete model of the Dirac-Kähler equation. Reports on Mathematical Physics 2014, 73, 109 -125.

AMA Style

Volodymyr Sushch. A discrete model of the Dirac-Kähler equation. Reports on Mathematical Physics. 2014; 73 (1):109-125.

Chicago/Turabian Style

Volodymyr Sushch. 2014. "A discrete model of the Dirac-Kähler equation." Reports on Mathematical Physics 73, no. 1: 109-125.

Book chapter
Published: 29 July 2013 in Springer Texts in Business and Economics
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We study discrete models which are generated by the self-dual Yang–Mills equations. Using a double complex construction, we construct a new discrete analog of the Bogomolny equations. Discrete Bogomolny equations, a system of matrix-valued difference equations, are obtained from discrete self-dual equations. The gauge invariance of the discrete model is established.

ACS Style

Volodymyr Sushch. A Double Complex Construction and Discrete Bogomolny Equations. Springer Texts in Business and Economics 2013, 47, 615 -624.

AMA Style

Volodymyr Sushch. A Double Complex Construction and Discrete Bogomolny Equations. Springer Texts in Business and Economics. 2013; 47 ():615-624.

Chicago/Turabian Style

Volodymyr Sushch. 2013. "A Double Complex Construction and Discrete Bogomolny Equations." Springer Texts in Business and Economics 47, no. : 615-624.

Journal article
Published: 21 November 2012 in Journal of Mathematical Sciences
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A discrete model of Bogomolny equations based on the combinatorial structure of a double complex is constructed. It is shown that the difference analogs of the Bogomolny equations can be obtained from the discrete self-dual Yang–Mills equations and preserve the geometric properties of the corresponding equations of continual theory.

ACS Style

Volodymyr Sushch. A discrete analog of the Bogomolny equations. Journal of Mathematical Sciences 2012, 187, 574 -582.

AMA Style

Volodymyr Sushch. A discrete analog of the Bogomolny equations. Journal of Mathematical Sciences. 2012; 187 (5):574-582.

Chicago/Turabian Style

Volodymyr Sushch. 2012. "A discrete analog of the Bogomolny equations." Journal of Mathematical Sciences 187, no. 5: 574-582.

Journal article
Published: 01 January 2012 in Mathematica Bohemica
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We study a discrete model of the $SU(2)$ Yang-Mills equations on a combinatorial analog of $\mathbb {R}^4$. Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both the techniques of a double complex and the quaternionic approach.

ACS Style

Volodymyr Sushch. Instanton-anti-instanton solutions of discrete Yang-Mills equations. Mathematica Bohemica 2012, 137, 219 -228.

AMA Style

Volodymyr Sushch. Instanton-anti-instanton solutions of discrete Yang-Mills equations. Mathematica Bohemica. 2012; 137 (2):219-228.

Chicago/Turabian Style

Volodymyr Sushch. 2012. "Instanton-anti-instanton solutions of discrete Yang-Mills equations." Mathematica Bohemica 137, no. 2: 219-228.

Journal article
Published: 01 January 2010 in Cubo (Temuco)
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We study a discrete model of the SU(2) Yang-Mills equations on a combinatorial analog of $Bbb{R}^4$. Self-dual and anti-self-dual solutions of discrete Yang-Mills equations are constructed. To obtain these solutions we use both techniques of a double complex and the quaternionic approach. Interesting analogies between instanton, anti-instanton solutions of discrete and continual self-dual, anti-self-dual equations are also discussed.

ACS Style

Volodymyr Sushch. Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex. Cubo (Temuco) 2010, 12, 99 -120.

AMA Style

Volodymyr Sushch. Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex. Cubo (Temuco). 2010; 12 (3):99-120.

Chicago/Turabian Style

Volodymyr Sushch. 2010. "Self-Dual and Anti-Self-Dual Solutions of Discrete Yang-Mills Equations on a Double Complex." Cubo (Temuco) 12, no. 3: 99-120.

Journal article
Published: 23 June 2009 in Journal of Mathematical Sciences
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We prove essential self-adjointness for a semibounded from below discrete magnetic Schrödinger operator in a space that represents a combinatorial model of the two-dimensional Euclidean space. The Dezin discretization scheme is used for constructing a discrete model.

ACS Style

V. N. Sushch. Essential self-adjointness of a discrete magnetic Schrödinger operator. Journal of Mathematical Sciences 2009, 160, 368 -378.

AMA Style

V. N. Sushch. Essential self-adjointness of a discrete magnetic Schrödinger operator. Journal of Mathematical Sciences. 2009; 160 (3):368-378.

Chicago/Turabian Style

V. N. Sushch. 2009. "Essential self-adjointness of a discrete magnetic Schrödinger operator." Journal of Mathematical Sciences 160, no. 3: 368-378.

Book chapter
Published: 01 September 2000 in Equadiff 99
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Some method of constructing intrinsically defined discrete models for differential operators on the space with the Lorentz metric is described. The difference wave equation and a discrete model of the mixed problem are constructed.

ACS Style

Volodymyr Sushch. On discrete models of the wave equation. Equadiff 99 2000, 354 -356.

AMA Style

Volodymyr Sushch. On discrete models of the wave equation. Equadiff 99. 2000; ():354-356.

Chicago/Turabian Style

Volodymyr Sushch. 2000. "On discrete models of the wave equation." Equadiff 99 , no. : 354-356.

Journal article
Published: 01 August 1999 in Journal of Mathematical Sciences
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We study optimal control problems with a quadratic optimization criterion. The state of the system is described by the solution of an operator-differential equation under nonlocal boundary conditions; the control is on the righth- and side of the equation. We prove existence and uniqueness theorems for the optimal control.

ACS Style

V. N. Sushch. Distributed control in a class of nonlocal boundary-value problems. Journal of Mathematical Sciences 1999, 96, 2838 -2842.

AMA Style

V. N. Sushch. Distributed control in a class of nonlocal boundary-value problems. Journal of Mathematical Sciences. 1999; 96 (1):2838-2842.

Chicago/Turabian Style

V. N. Sushch. 1999. "Distributed control in a class of nonlocal boundary-value problems." Journal of Mathematical Sciences 96, no. 1: 2838-2842.

Journal article
Published: 01 May 1997 in Mathematical Notes of the Academy of Sciences of the USSR
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Two discrete models of Yang-Mill equations are constructed in the space ℝn for some matrix-valued Lie group. A gauge-invariant discrete model is examined.

ACS Style

V. N. Sushch. Gauge-invariant discrete models of Yang-Mills equations. Mathematical Notes of the Academy of Sciences of the USSR 1997, 61, 621 -631.

AMA Style

V. N. Sushch. Gauge-invariant discrete models of Yang-Mills equations. Mathematical Notes of the Academy of Sciences of the USSR. 1997; 61 (5):621-631.

Chicago/Turabian Style

V. N. Sushch. 1997. "Gauge-invariant discrete models of Yang-Mills equations." Mathematical Notes of the Academy of Sciences of the USSR 61, no. 5: 621-631.

Journal article
Published: 01 October 1993 in Journal of Mathematical Sciences
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We study the problem of optimal control with a quadratic optimization criterion. The state of the system is described by operator-differential equations with nonlocal boundary conditions. We prove an existence and uniqueness theorem for an optimal control.

ACS Style

Volodymyr Sushch. Nonlocal problems with boundary controls. Journal of Mathematical Sciences 1993, 66, 2595 -2600.

AMA Style

Volodymyr Sushch. Nonlocal problems with boundary controls. Journal of Mathematical Sciences. 1993; 66 (6):2595-2600.

Chicago/Turabian Style

Volodymyr Sushch. 1993. "Nonlocal problems with boundary controls." Journal of Mathematical Sciences 66, no. 6: 2595-2600.