M. Paukshto - Academia.edu (original) (raw)

Papers by M. Paukshto

Research paper thumbnail of Approximate Solution of Integral Equations

TEUBNER-TEXTE zur Mathematik, 1995

Finite difference methods, widely employed for the solution of differential (or other operator) e... more Finite difference methods, widely employed for the solution of differential (or other operator) equations are also used to solve approximately integral equations; they include the methods of Ritz, Bubnov-Galerkin, least squares, collocation as well as a variety of these methods, linked to the application of so called finite elements. One has also been made of grid methods which, in the case of integral equations, assume the form of “methods of mechanical quadrature”. The method of iteration has been applied for the solution of equations of the form u − Au = f, ║A║ < 1.

Research paper thumbnail of On some applications of integral equations in elasticity

Integral methods in science and engineering, 2020

Research paper thumbnail of Direct schemes of the potential theory

Research paper thumbnail of Application specific polarizer

Research paper thumbnail of Behavior of cells on tissue-like collagen matrices

1. Fibralign Corp., Sunnyvale, CA, USA; 2. NIH, Bethesda, MD, USA; 3. Physiology, UCSF, San Franc... more 1. Fibralign Corp., Sunnyvale, CA, USA; 2. NIH, Bethesda, MD, USA; 3. Physiology, UCSF, San Francisco, CA, USA; 4. Periodontology, UCSF, San Francisco, CA, USA; 5. Cell Sciences Imaging Facility, Stanford University, Stanford, CA, USA; 6. College of Dentistry, NYU, New York, NY, USA. ABSTRACT. Using a novel computer controlled process, we have prepared sheets of collagen from soluble collagen which have skin-like, tendon-like, or an aligned braided structure on glass and plastic substrates. The process provides uniform structures over large area as confirmed by AFM, SEM, laser diffraction, and polarized microscopy. In some experiments, parallel microgrooves have been created during the deposition process while preserving fibril structure. Various cell types when plated on these matrices preferentially align and migrate along the fibrils or along the crimped ridges depending on the geometrical parameters of the surface nanostructure, including fibroblasts, stem cells (adipose-derived...

Research paper thumbnail of Two-Dimensional Singular Integral Equations

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of Piezoelectric properties of aligned collagen membranes

Journal of Biomedical Materials Research Part B: Applied Biomaterials, 2013

Electromechanical coupling, a phenomenon present in collagenous materials, may influence cellextr... more Electromechanical coupling, a phenomenon present in collagenous materials, may influence cellextracellular matrix interactions. Here, electromechanical coupling has been investigated via piezoresponse force microscopy in transparent and opaque collagen membranes consisting of helical-like arrays of aligned type I collagen fibrils self-assembled from acidic collagen solution. Using atomic force microscopy, the transparent membrane was determined to contain fibrils having an average diameter of 76 ± 14 nm, while the opaque membrane comprised fibrils with an average diameter of 391 ± 99 nm. As the acidity of the membranes must be neutralized before they can serve as cell culture substrates, the structure and piezoelectric properties of the membranes were measured under ambient conditions before and after the neutralization process. A crimp structure (1.59 ± 0.37 µm in width) perpendicular to the fibril alignment became apparent in the transparent when the pH was adjusted from acidic (pH = 2.5) to neutral (pH = 7) conditions. In addition, a 1.35 fold increase was observed in the amplitude of the shear piezoelectricity of the transparent membrane. The structure and piezoelectric properties of the opaque membrane were not significantly affected by the neutralization process. The results highlight the presence of an additional translational order in the transparent membrane in the direction perpendicular to the fibril alignment. The piezoelectric response of both membrane types was found to be an order of magnitude lower than that of collagen fibrils in rat tail tendon. This reduced response is attributed to less-ordered molecular assembly than is present in Dperiodic collagen fibrils, as evidenced by the absence of D-periodicity in the membranes.

Research paper thumbnail of Problems of the Theory of Cracks

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of General Results on Linear Integral Equations

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of Potential Theory for Basic Three-Dimensional Problems

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of The Contact Problems of the Theory of Elasticity

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of P-92: Enhanced Viewing Angle Characteristics: Compensated TN Design with E-type Polarizers

SID Symposium Digest of Technical Papers, 2002

Research paper thumbnail of P-92: Enhanced Viewing Angle Characteristics: Compensated TN Design with E-type Polarizers

SID Symposium Digest of Technical Papers, 2002

Research paper thumbnail of An extension theorem for certain functional classes

Mathematical Notes of the Academy of Sciences of the USSR, 1979

I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined... more I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined in the following manner:

Research paper thumbnail of An extension theorem for certain functional classes

Mathematical Notes of the Academy of Sciences of the USSR, 1979

I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined... more I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined in the following manner:

Research paper thumbnail of The wedge paradox and a correspondence principle

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is th... more Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is the wedge loaded by a concentrated moment at the vertex (Carothers problem). The paradox consists of the fact the for wedges smaller than a half-space the solution exists, while for ...

Research paper thumbnail of The wedge paradox and a correspondence principle

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is th... more Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is the wedge loaded by a concentrated moment at the vertex (Carothers problem). The paradox consists of the fact the for wedges smaller than a half-space the solution exists, while for ...

Research paper thumbnail of The Cosserat spectrum in the theory of elasticity and applications

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of C... more By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA 2Institute of Mathematics and Mechanics, Saint Petersburg State University, 198328, Box 125, St Petersburg, Russia

Research paper thumbnail of The Cosserat spectrum in the theory of elasticity and applications

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of C... more By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA 2Institute of Mathematics and Mechanics, Saint Petersburg State University, 198328, Box 125, St Petersburg, Russia

Research paper thumbnail of On the Cavities and Rigid Inclusions Correspondence and the Cosserat Spectrum

Mathematische Nachrichten, 1996

Research paper thumbnail of Approximate Solution of Integral Equations

TEUBNER-TEXTE zur Mathematik, 1995

Finite difference methods, widely employed for the solution of differential (or other operator) e... more Finite difference methods, widely employed for the solution of differential (or other operator) equations are also used to solve approximately integral equations; they include the methods of Ritz, Bubnov-Galerkin, least squares, collocation as well as a variety of these methods, linked to the application of so called finite elements. One has also been made of grid methods which, in the case of integral equations, assume the form of “methods of mechanical quadrature”. The method of iteration has been applied for the solution of equations of the form u − Au = f, ║A║ < 1.

Research paper thumbnail of On some applications of integral equations in elasticity

Integral methods in science and engineering, 2020

Research paper thumbnail of Direct schemes of the potential theory

Research paper thumbnail of Application specific polarizer

Research paper thumbnail of Behavior of cells on tissue-like collagen matrices

1. Fibralign Corp., Sunnyvale, CA, USA; 2. NIH, Bethesda, MD, USA; 3. Physiology, UCSF, San Franc... more 1. Fibralign Corp., Sunnyvale, CA, USA; 2. NIH, Bethesda, MD, USA; 3. Physiology, UCSF, San Francisco, CA, USA; 4. Periodontology, UCSF, San Francisco, CA, USA; 5. Cell Sciences Imaging Facility, Stanford University, Stanford, CA, USA; 6. College of Dentistry, NYU, New York, NY, USA. ABSTRACT. Using a novel computer controlled process, we have prepared sheets of collagen from soluble collagen which have skin-like, tendon-like, or an aligned braided structure on glass and plastic substrates. The process provides uniform structures over large area as confirmed by AFM, SEM, laser diffraction, and polarized microscopy. In some experiments, parallel microgrooves have been created during the deposition process while preserving fibril structure. Various cell types when plated on these matrices preferentially align and migrate along the fibrils or along the crimped ridges depending on the geometrical parameters of the surface nanostructure, including fibroblasts, stem cells (adipose-derived...

Research paper thumbnail of Two-Dimensional Singular Integral Equations

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of Piezoelectric properties of aligned collagen membranes

Journal of Biomedical Materials Research Part B: Applied Biomaterials, 2013

Electromechanical coupling, a phenomenon present in collagenous materials, may influence cellextr... more Electromechanical coupling, a phenomenon present in collagenous materials, may influence cellextracellular matrix interactions. Here, electromechanical coupling has been investigated via piezoresponse force microscopy in transparent and opaque collagen membranes consisting of helical-like arrays of aligned type I collagen fibrils self-assembled from acidic collagen solution. Using atomic force microscopy, the transparent membrane was determined to contain fibrils having an average diameter of 76 ± 14 nm, while the opaque membrane comprised fibrils with an average diameter of 391 ± 99 nm. As the acidity of the membranes must be neutralized before they can serve as cell culture substrates, the structure and piezoelectric properties of the membranes were measured under ambient conditions before and after the neutralization process. A crimp structure (1.59 ± 0.37 µm in width) perpendicular to the fibril alignment became apparent in the transparent when the pH was adjusted from acidic (pH = 2.5) to neutral (pH = 7) conditions. In addition, a 1.35 fold increase was observed in the amplitude of the shear piezoelectricity of the transparent membrane. The structure and piezoelectric properties of the opaque membrane were not significantly affected by the neutralization process. The results highlight the presence of an additional translational order in the transparent membrane in the direction perpendicular to the fibril alignment. The piezoelectric response of both membrane types was found to be an order of magnitude lower than that of collagen fibrils in rat tail tendon. This reduced response is attributed to less-ordered molecular assembly than is present in Dperiodic collagen fibrils, as evidenced by the absence of D-periodicity in the membranes.

Research paper thumbnail of Problems of the Theory of Cracks

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of General Results on Linear Integral Equations

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of Potential Theory for Basic Three-Dimensional Problems

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of The Contact Problems of the Theory of Elasticity

TEUBNER-TEXTE zur Mathematik, 1995

Research paper thumbnail of P-92: Enhanced Viewing Angle Characteristics: Compensated TN Design with E-type Polarizers

SID Symposium Digest of Technical Papers, 2002

Research paper thumbnail of P-92: Enhanced Viewing Angle Characteristics: Compensated TN Design with E-type Polarizers

SID Symposium Digest of Technical Papers, 2002

Research paper thumbnail of An extension theorem for certain functional classes

Mathematical Notes of the Academy of Sciences of the USSR, 1979

I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined... more I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined in the following manner:

Research paper thumbnail of An extension theorem for certain functional classes

Mathematical Notes of the Academy of Sciences of the USSR, 1979

I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined... more I. In this article we will obtain an extension theorem for the functional classes l 0~v~, defined in the following manner:

Research paper thumbnail of The wedge paradox and a correspondence principle

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is th... more Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is the wedge loaded by a concentrated moment at the vertex (Carothers problem). The paradox consists of the fact the for wedges smaller than a half-space the solution exists, while for ...

Research paper thumbnail of The wedge paradox and a correspondence principle

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is th... more Received 4 February 1997; accepted 28 May 1997 The wedge paradox for stress-free boundaries is the wedge loaded by a concentrated moment at the vertex (Carothers problem). The paradox consists of the fact the for wedges smaller than a half-space the solution exists, while for ...

Research paper thumbnail of The Cosserat spectrum in the theory of elasticity and applications

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of C... more By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA 2Institute of Mathematics and Mechanics, Saint Petersburg State University, 198328, Box 125, St Petersburg, Russia

Research paper thumbnail of The Cosserat spectrum in the theory of elasticity and applications

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998

By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of C... more By Xanthippi Markenscoff1 and Michael Paukshto2 1Department of Applied Mechanics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA 2Institute of Mathematics and Mechanics, Saint Petersburg State University, 198328, Box 125, St Petersburg, Russia

Research paper thumbnail of On the Cavities and Rigid Inclusions Correspondence and the Cosserat Spectrum

Mathematische Nachrichten, 1996