Radiation resistance of epoxy resins

We have investigated the radiation resistance of epoxy resins cured with different curing agents—phthalic and maleic anhydrides, m-phenylenediamine, hexamethylenediamine, and triethanolamine titanate. Test data on the physicomechanical properties of these compositions are presented; the degree of variation of the gel fraction has been determined; thermomechanical curves and IR absorption spectra have been recorded. Conclusions are drawn concerning the mechanism of the radiochemical processes and it is shown that the nature of these processes and hence the nature and extent of the change in the physicomechanical properties of the materials—the cured epoxy compounds—primarily depend on the type of curing agent employed.Mekhanika Polimerov, Vol. 3, No. 3, pp. 476–482, 1967     

Some presentations for the special linear groups on finite fields

We simplify the Steinberg presentation of SL _n (F _d ), where n≥1 and F _d is any finite field with d elements. That presentation has the elementary matrices e _ij (r), with i,j∈{1,...,n}, i≠=j and r∈F _d , as generators, and (E1)–(E3), described at the opening of this work, as relations. The presentation that we shall obtain reduces the number of generators e _ij (r) and relations (E1)–(E3). In particular, relations (E3) are considerably reduced. Received: March 16, 1998; in final form: November 3, 2000?Published online: October 2, 2001     

Thermomagnetic convection under alternating magnetic fields

Thermomagnetic convection within a square cavity filled with a magnetic fluid was studied under alternating magnetic field. The aim was to explore the response of the magnetic fluid towards alternating magnetic fields. A set of frequencies for the sinusoidal variation of the magnetic field intensity was used to study the heat transfer characteristics across the problem geometry. The effect on heat transfer was quantified by an averaged Nusselt number. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tilting modules under special base changes

Given a non-unit, non-zero-divisor, central element x of a ring Λ, it is well known that many properties or invariants of Λ determine, and are determined by, those of $\mathrm{\Lambda }/x\mathrm{\Lambda }$ and ${\mathrm{\Lambda }}_x$. In the present paper, we investigate how the property of “being tilting” behaves in this situation. It turns out that any tilting module over Λ gives rise to tilting modules over ${\mathrm{\Lambda }}_x$ and $\mathrm{\Lambda }/x\mathrm{\Lambda }$ after localization and passing to quotient respectively. On the other hand, it is proved that under some mild conditions, a module over Λ is tilting if its corresponding localization and quotient are tilting over ${\mathrm{\Lambda }}_x$ and $\mathrm{\Lambda }/x\mathrm{\Lambda }$ respectively.     

Radiation resistance of epoxy and epoxytriazine resins

We have investigated the nature and extent of the changes in the physicomechanical and thermomechanical properties of epoxy and epoxytriazine compositions resulting from exposure to Co⁶⁰ -radiation. The effect of active solvents and catalysts on the radiation resistance of these compositions has been determined. Conclusions are reached concerning the nature of the radiochemical processes involved.Mekhanika Polimerov, Vol. 3, No. 5, pp. 840–845, 1967     

Magnetohydrodynamic duct flow under circular and radial magnetic fields

Zusammenfassung Es werden für die Strömung einer elektrisch leitenden Flüssigkeit in einem ringsektorförmigen Kanal genaue Lösungen gegeben, wobei ein radiales oder tangentielles Magnetfeld angesetzt wird und die Wände vollkommene Leiter oder Isolatoren sind. Eine Grenzschicht-Analyse wird für grosse Hartmann-Zahl durchgeführt. Die bekannten Lösungen für den rechteckigen Kanal unter einem gleichmässigen transversalen Feld folgen als Sonderfälle. Die Resultate werden graphisch dargestellt.     

Effect of an electron beam on the structure of epoxy resins

It is shown that exposing a cured epoxy resin to the action of an electron beam leads to a change in the structure outside the zone of direct action of the beam; this is accompanied by the formation of diffraction rings in the electron diffraction pattern and a change in microhardness.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 523–525, May–June, 1976.     

A basic relation between invariants of matrices under the action of the special orthogonal group

The first fundamental theorem of invariant theory for the action of the special orthogonal group onm tuples of matrices by simultaneous conjugation is proved in [2]. In this paper, as a first step in the direction of establishing the second fundamental theorem, we study a basic identity betweenSO(n, K) invariants ofm matrices.     

Interfacial model for crash resistant adhesives of ductile-modified epoxy resins

Debonding in adhesive joints is modelled and analyzed with the concept of interfacial mechanics. Material equations are presented for the inelastic behaviour of ductile-modified epoxy resins. A two surface function for the onset of yielding is advantageously expressed in terms of the stress vector on the interface. The theory may be extended to material softening due to damage and to rate dependency. This simple constitutive model is not stable in the sense of Drucker's postulate. Therefore, the non-associated flow rule is modified with a quadratic stress-dependent plastic potential. The material parameters are identified by means of the finite-element simulation of the experimental setup for a bluntly glued double steel tube sample. The numerical performance of this modified model is tested at an adhesively bonded joint in the form of a T-intersection. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stability of nematic liquid crystals under crossed electric and magnetic fields

The alignment of the director in nematic liquid crystals is known to be influenced by electric and/or magnetic fields. The stability of known traveling wave solutions is examined for a best fit cubic equation which approximates the nonlinear sinusoidal terms in the dynamic equation for the director when it is subjected to crossed electric and magnetic fields.     

Double diffusive convection in porous media under the action of a magnetic field

The onset of thermal convection in an electrically conducting fluid saturating a porous medium, uniformly heated from below, salted by one chemical and embedded in an external transverse magnetic field is analyzed. The critical Rayleigh thermal numbers at which steady and Hopf convection can occur, are determined. Sufficient conditions guaranteeing the effective onset of convection via steady or oscillatory state are provided.

     

Some closed form formulae for the intersection of two special matrices under the star order

In this note we present closed form formulae for the intersection A ∧ B under the star order, for certain pairs of special matrices. In particular, it is shown that for two m×n partial isometries P and QP∧Q=P[I-(I-P^*Q)^†(I-P^*Q)]. Some further possible representations for P∧Q are considered.     

Some features of bone tissue deformation under unloading and repeated laoding

Conclusions 1. There is a change in the initial elastic properties of compact bone tissue when a load is removed after repeated loading.2. The elasticity modulus after the load has been removed can be assumed to be independent of the level of stress _11k at which the load was removed.3. With repeat loadings, the tangential elastic modulus increases for the same level of stress when the off-loading stress _11k is increased.4. The value of the irreversible expended specific energy of deformation W increases sharply as the moment of destruction approaches, while its distribution through the zones of the cross section of bone provides good rheological adaptation of the bone to external loads in human walking.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 882–890, September–October, 1976.     

Some special solutions of the Helmholtz equation

Functions are constructed which describe a cylindrical wave diverging from the origin and tangent to a semi-infinite plane wave. The use of such functions is illustrated by the example of the problem of diffraction of a plane wave by a semi-infinite screen.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 51, pp. 197–202, 1975.