5,127 research outputs found
Lower bound for LCF lifetime and its application to safe design of elastic viscoplastic structures
AbstractThe theory of shakedown is applied to obtain an upper estimation of LCF lifetime of structures. A model of elastic viscoplastic material similar to the Perzyna one with isotropic strain hardening and isotropic damage is adopted. Assumptions: viscoplastic strain rate is proportional to the access of the yield function over zero; the rate of damage evolution is equal to a function of hardening and damage parameters with the coefficient of fluidity, as a factor of proportionality; damage process is coupled with the viscoplastic deformation process; the hardening parameter is equal to accumulated viscoplastic deformation. The yield surfaces form a family of self-similar surfaces with the diameter as the parameter. The shakedown condition of the Melan type is formulated relatively to the initial yield surface. Features of the stress path lead to an equation with minβmax problem of the mathematical programming in the left side, which determines a safe value of the virtual residual stress. The equation provides an opportunity to compute the maximal value of the strain hardening parameter possible under the prescribed loading program. This value allows to obtain an upper estimate to safe work time of the structure, which results in a sufficient condition of the structure integrity during the prescribed time period. An example of the developed theory application to resolve various problems arising from designing of structures is considered
First quantized approaches to neutrino oscillations and second quantization
Neutrino oscillations are treated from the point of view of relativistic
first quantized theories and compared to second quantized treatments. Within
first quantized theories, general oscillation probabilities can be found for
Dirac fermions and charged spin 0 bosons. A clear modification in the
oscillation formulas can be obtained and its origin is elucidated and confirmed
to be inevitable from completeness and causality requirements. The left-handed
nature of created and detected neutrinos can also be implemented in the first
quantized Dirac theory in presence of mixing; the probability loss due to the
changing of initially left-handed neutrinos to the undetected right-handed
neutrinos can be obtained in analytic form. Concerning second quantized
approaches, it is shown in a calculation using virtual neutrino propagation
that both neutrinos and antineutrinos may also contribute as intermediate
particles. The sign of the contributing neutrino energy may have to be chosen
explicitly without being automatic in the formalism. At last, a simple second
quantized description of the flavor oscillation phenomenon is devised. In this
description there is no interference terms between positive and negative
components, but it still gives simple normalized oscillation probabilities. A
new effect appearing in this context is an inevitable but tiny violation of the
initial flavor of neutrinos. The probability loss due to the conversion of
left-handed neutrinos to right-handed neutrinos is also presented.Comment: version accepted for publicatio
ΠΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π±Π°Π·ΠΎΠ²ΡΡ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ ΠΊΡΠΈΡΠ΅ΡΠΈΠ΅Π²
Π Π°Π·Π½ΠΎΠΎΠ±ΡΠ°Π·ΠΈΠ΅ ΠΏΡΠΈΡΠΎΠ΄Π½ΠΎ-ΠΊΠ»ΠΈΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΈ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΡΠΎΡΡΠΈΠΉΡΠΊΠΈΡ
ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ² ΠΏΡΠ΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅Ρ ΡΠΈΡΠΎΠΊΠΈΠΉ Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ΠΎΠ² ΠΊ ΠΈΡ
ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. ΠΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎ ΡΡΠ»ΠΎΠΆΠ½ΡΠ΅ΡΡΡ Π·Π°Π΄Π°ΡΠ° Π°Π±ΡΡΡΠ°Π³ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ Π»ΡΠ±ΠΎΠΉ ΠΎΡΡΠ°ΡΠ»ΠΈ Π½Π°ΡΠΎΠ΄Π½ΠΎΠ³ΠΎ Ρ
ΠΎΠ·ΡΠΉΡΡΠ²Π°. ΠΡΡΠ΅ΠΊΡΠΈΠ²Π½Π°Ρ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ Π²Π°ΠΆΠ½Π° ΡΠ°ΠΊΠΆΠ΅ Π² ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΈΠ·ΡΡΠ΅Π½Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ Π±Π°Π·ΠΎΠ²ΠΎΠΉ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΡΠ΄ΠΎΠ² ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΠΈ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Ρ
ΠΎΠ·ΡΠΉΡΡΠ²Π°. ΠΠΎΠ²ΠΈΠ·Π½Π° ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π½Π°Π±Π»ΡΠ΄Π°ΡΡ ΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°ΡΡ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ Π² ΠΌΠ΅Π·ΠΎΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΠΏΠΎΡΡΠΈΡΡ
. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΎΡΠΈΡΠΈΠ°Π»ΡΠ½ΡΡ
Π΄Π°Π½Π½ΡΡ
Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΡΡΠ°ΡΠΈΡΡΠΈΠΊΠΈ ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½Ρ Π³ΡΡΠΏΠΏΡ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΠΏΠΎ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎΠΌΡ, ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎ-ΠΈΠ½ΡΡΠΈΡΡΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΌΡ ΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎ-ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΌΡ ΠΊΡΠΈΡΠ΅ΡΠΈΡΠΌ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π²ΡΠ±ΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ Β«k-ΡΡΠ΅Π΄Π½Π΅Π΅Β». ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΠ΅Ρ
ΡΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
ΡΠ΅Π³ΠΌΠ΅Π½ΡΠΎΠ² ΡΠ°ΡΡΡΠΈΡΠ°Π½Ρ ΡΡΠ΅Π΄Π½ΠΈΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΏΠΎ ΠΈΡΡ
ΠΎΠ΄Π½ΡΠΌ ΠΏΡΠΈΠ·Π½Π°ΠΊΠ°ΠΌ. Π‘Π΅Π³ΠΌΠ΅Π½ΡΡ ΠΊΠ»Π°ΡΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Ρ Ρ ΠΏΠΎΠ·ΠΈΡΠΈΠΉ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ. ΠΡΠ΄Π΅Π»ΡΠ½ΠΎ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΡΡΠ±ΡΠ΅ΠΊΡΡ-Π²ΡΠ±ΡΠΎΡΡ, Π΄Π°Π»Π΅ΠΊΠΎ ΠΎΡΡΡΠΎΡΡΠΈΠ΅ ΠΎΡ ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΌΠ°ΡΡΠΈΠ²ΠΎΠ² Π΄Π°Π½Π½ΡΡ
. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠ΄ΠΈΠ»ΠΈ ΡΠΈΡΠΎΠΊΠΎΠ΅ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ², Π²Ρ
ΠΎΠ΄ΡΡΠΈΡ
Π² ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅Π³ΠΌΠ΅Π½ΡΡ. ΠΠ°Π½Π½Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ Π±ΡΠ΄Π΅Ρ ΠΏΠΎΠ»Π΅Π·Π½Π° ΠΏΡΠΈ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΉ ΠΈ Π²ΡΠ±ΠΎΡΠ΅ ΠΈΠ½ΡΡΡΡΠΌΠ΅Π½ΡΠΎΠ² Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ, ΡΡΡΠ°ΡΠ΅Π³ΠΈΠΈ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΡ
ΠΊΠ»Π°ΡΡΠ΅ΡΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠΈ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ°Π±ΠΎΡΡ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠ³ΠΎ Π°Π³ΡΠΎΠ±ΠΈΠ·Π½Π΅ΡΠ°, ΡΡΡΡΠ°Π½Π΅Π½ΠΈΠΈ ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠΈΡ
Π΄ΠΈΡΠΏΡΠΎΠΏΠΎΡΡΠΈΠΉ Π² Π΅Π³ΠΎ ΡΠ°Π·Π²ΠΈΡΠΈΠΈ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠ΅Π³ΠΎ ΡΠΎΠ²Π΅ΡΡΠ΅Π½ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΠΈ Π² Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠ΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ ΡΠ°ΡΡΠΈΡΠΈΡΡ Π°Π½Π°Π»ΠΈΠ· Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΈΠ·ΡΡΠ°Π΅ΠΌΠΎΠ³ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ½ΡΠ΅ΡΠ²Π°Π»Π°, ΡΠΎΡΡΠ° ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° Π²ΠΊΠ»ΡΡΠ°Π΅ΠΌΡΡ
Π² ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ°ΠΊΡΠΎΡΠΎΠ² ΠΈ ΠΈΡ
Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠΉ, Π²Π²Π΅Π΄Π΅Π½ΠΈΡ Π½ΠΎΠ²ΡΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ. ΠΠ°Π½Π½ΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΌΠΎΠΆΠ½ΠΎ Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΏΡΠΈΠΌΠ΅Π½ΡΡΡ Π΄Π»Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΎΠ² ΡΡΡΡΠΊΡΡΡΠ½ΡΡ
ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ ΠΈ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π°
ΠΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ² Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π±Π°Π·ΠΎΠ²ΡΡ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ ΠΊΡΠΈΡΠ΅ΡΠΈΠ΅Π²
Π Π°Π·Π½ΠΎΠΎΠ±ΡΠ°Π·ΠΈΠ΅ ΠΏΡΠΈΡΠΎΠ΄Π½ΠΎ-ΠΊΠ»ΠΈΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΈ ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΡΡΠ»ΠΎΠ²ΠΈΠΉ ΡΠΎΡΡΠΈΠΉΡΠΊΠΈΡ
ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ² ΠΏΡΠ΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅Ρ ΡΠΈΡΠΎΠΊΠΈΠΉ Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠ΄Ρ
ΠΎΠ΄ΠΎΠ² ΠΊ ΠΈΡ
ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΠΈ. ΠΠ΄Π½ΠΎΠ²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎ ΡΡΠ»ΠΎΠΆΠ½ΡΠ΅ΡΡΡ Π·Π°Π΄Π°ΡΠ° Π°Π±ΡΡΡΠ°Π³ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ Π»ΡΠ±ΠΎΠΉ ΠΎΡΡΠ°ΡΠ»ΠΈ Π½Π°ΡΠΎΠ΄Π½ΠΎΠ³ΠΎ Ρ
ΠΎΠ·ΡΠΉΡΡΠ²Π°. ΠΡΡΠ΅ΠΊΡΠΈΠ²Π½Π°Ρ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡ Π²Π°ΠΆΠ½Π° ΡΠ°ΠΊΠΆΠ΅ Π² ΠΏΡΠΎΡΠ΅ΡΡΠ΅ ΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ. Π ΡΠ°Π±ΠΎΡΠ΅ ΠΈΠ·ΡΡΠ΅Π½Ρ Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΠΈ Π±Π°Π·ΠΎΠ²ΠΎΠΉ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΉ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΡΡ
ΡΡΠ΄ΠΎΠ² ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΠΈ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΡΠ°Π·Π²ΠΈΡΠΈΡ ΡΠ΅Π»ΡΡΠΊΠΎΠ³ΠΎ Ρ
ΠΎΠ·ΡΠΉΡΡΠ²Π°. ΠΠΎΠ²ΠΈΠ·Π½Π° ΠΏΡΠ΅Π΄Π»Π°Π³Π°Π΅ΠΌΠΎΠ³ΠΎ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Π° Π·Π°ΠΊΠ»ΡΡΠ°Π΅ΡΡΡ Π² ΠΌΠ΅ΡΠΎΠ΄ΠΈΠΊΠ΅ Π΄ΠΈΠ½Π°ΠΌΠΈΡΠ΅ΡΠΊΠΎΠ³ΠΎ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½ΠΈΡ, ΠΊΠΎΡΠΎΡΠ°Ρ ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ Π½Π°Π±Π»ΡΠ΄Π°ΡΡ ΠΈ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΈΡΠΎΠ²Π°ΡΡ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠ΅ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ Π² ΠΌΠ΅Π·ΠΎΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΡΠΎΠΏΠΎΡΡΠΈΡΡ
. ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΠΎΡΠΈΡΠΈΠ°Π»ΡΠ½ΡΡ
Π΄Π°Π½Π½ΡΡ
Π³ΠΎΡΡΠ΄Π°ΡΡΡΠ²Π΅Π½Π½ΠΎΠΉ ΡΡΠ°ΡΠΈΡΡΠΈΠΊΠΈ ΡΡΠΎΡΠΌΠΈΡΠΎΠ²Π°Π½Ρ Π³ΡΡΠΏΠΏΡ ΠΏΠΎΠΊΠ°Π·Π°ΡΠ΅Π»Π΅ΠΉ ΠΏΠΎ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎΠΌΡ, ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎ-ΠΈΠ½ΡΡΠΈΡΡΡΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠΌΡ ΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΠΎ-ΡΡΡΡΠΊΡΡΡΠ½ΠΎΠΌΡ ΠΊΡΠΈΡΠ΅ΡΠΈΡΠΌ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ ΠΎΡΠ½ΠΎΠ²Π½ΠΎΠ³ΠΎ ΠΌΠ΅ΡΠΎΠ΄Π° ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ Π²ΡΠ±ΡΠ°Π½ ΠΌΠ΅ΡΠΎΠ΄ ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ Β«k-ΡΡΠ΅Π΄Π½Π΅Π΅Β». ΠΠ° ΠΎΡΠ½ΠΎΠ²Π΅ ΡΡΠ΅Ρ
ΡΠΌΠΎΠ΄Π΅Π»ΠΈΡΠΎΠ²Π°Π½Π½ΡΡ
ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΡΡ
ΡΠ΅Π³ΠΌΠ΅Π½ΡΠΎΠ² ΡΠ°ΡΡΡΠΈΡΠ°Π½Ρ ΡΡΠ΅Π΄Π½ΠΈΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΏΠΎ ΠΈΡΡ
ΠΎΠ΄Π½ΡΠΌ ΠΏΡΠΈΠ·Π½Π°ΠΊΠ°ΠΌ. Π‘Π΅Π³ΠΌΠ΅Π½ΡΡ ΠΊΠ»Π°ΡΡΠΈΡΠΈΡΠΈΡΠΎΠ²Π°Π½Ρ Ρ ΠΏΠΎΠ·ΠΈΡΠΈΠΉ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊ. ΠΡΠ΄Π΅Π»ΡΠ½ΠΎ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½Ρ ΡΡΠ±ΡΠ΅ΠΊΡΡ-Π²ΡΠ±ΡΠΎΡΡ, Π΄Π°Π»Π΅ΠΊΠΎ ΠΎΡΡΡΠΎΡΡΠΈΠ΅ ΠΎΡ ΠΎΡΠ½ΠΎΠ²Π½ΡΡ
ΠΌΠ°ΡΡΠΈΠ²ΠΎΠ² Π΄Π°Π½Π½ΡΡ
. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΠΏΠΎΠ΄ΡΠ²Π΅ΡΠ΄ΠΈΠ»ΠΈ ΡΠΈΡΠΎΠΊΠΎΠ΅ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΡΠ΅Π³ΠΈΠΎΠ½ΠΎΠ², Π²Ρ
ΠΎΠ΄ΡΡΠΈΡ
Π² ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΡΠ΅ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅Π³ΠΌΠ΅Π½ΡΡ. ΠΠ°Π½Π½Π°Ρ ΠΊΠ»Π°ΡΡΠΈΡΠΈΠΊΠ°ΡΠΈΡ Π±ΡΠ΄Π΅Ρ ΠΏΠΎΠ»Π΅Π·Π½Π° ΠΏΡΠΈ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ Π½Π°ΠΏΡΠ°Π²Π»Π΅Π½ΠΈΠΉ ΠΈ Π²ΡΠ±ΠΎΡΠ΅ ΠΈΠ½ΡΡΡΡΠΌΠ΅Π½ΡΠΎΠ² Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΈ, ΡΡΡΠ°ΡΠ΅Π³ΠΈΠΈ ΡΠΎΠ·Π΄Π°Π½ΠΈΡ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π΅Π½Π½ΡΡ
ΠΊΠ»Π°ΡΡΠ΅ΡΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΠΏΡΠΈ ΠΏΠ»Π°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ°Π±ΠΎΡΡ ΡΠ΅Π³ΠΈΠΎΠ½Π°Π»ΡΠ½ΠΎΠ³ΠΎ Π°Π³ΡΠΎΠ±ΠΈΠ·Π½Π΅ΡΠ°, ΡΡΡΡΠ°Π½Π΅Π½ΠΈΠΈ ΡΡΡΠ΅ΡΡΠ²ΡΡΡΠΈΡ
Π΄ΠΈΡΠΏΡΠΎΠΏΠΎΡΡΠΈΠΉ Π² Π΅Π³ΠΎ ΡΠ°Π·Π²ΠΈΡΠΈΠΈ. Π ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π΄Π°Π»ΡΠ½Π΅ΠΉΡΠ΅Π³ΠΎ ΡΠΎΠ²Π΅ΡΡΠ΅Π½ΡΡΠ²ΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΠΈ Π°Π³ΡΠ°ΡΠ½ΠΎ-ΡΠΊΠΎΠ½ΠΎΠΌΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π³ΠΌΠ΅Π½ΡΠ°ΡΠΈΠΈ Π² Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠ΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ ΡΠ°ΡΡΠΈΡΠΈΡΡ Π°Π½Π°Π»ΠΈΠ· Ρ ΠΏΠΎΠΌΠΎΡΡΡ ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΡ ΠΈΠ·ΡΡΠ°Π΅ΠΌΠΎΠ³ΠΎ Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠ³ΠΎ ΠΈΠ½ΡΠ΅ΡΠ²Π°Π»Π°, ΡΠΎΡΡΠ° ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π° Π²ΠΊΠ»ΡΡΠ°Π΅ΠΌΡΡ
Π² ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠ°ΠΊΡΠΎΡΠΎΠ² ΠΈ ΠΈΡ
Π²Π·Π°ΠΈΠΌΠΎΠ΄Π΅ΠΉΡΡΠ²ΠΈΠΉ, Π²Π²Π΅Π΄Π΅Π½ΠΈΡ Π½ΠΎΠ²ΡΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΠΊΠ»Π°ΡΡΠ΅ΡΠΈΠ·Π°ΡΠΈΠΈ. ΠΠ°Π½Π½ΡΡ ΠΌΠΎΠ΄Π΅Π»Ρ ΠΌΠΎΠΆΠ½ΠΎ Π΄ΠΎΠΏΠΎΠ»Π½ΠΈΡΠ΅Π»ΡΠ½ΠΎ ΠΏΡΠΈΠΌΠ΅Π½ΡΡΡ Π΄Π»Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΡ ΠΏΡΠΎΠ³Π½ΠΎΠ·ΠΎΠ² ΡΡΡΡΠΊΡΡΡΠ½ΡΡ
ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ ΠΈ Π΄ΠΈΠ½Π°ΠΌΠΈΠΊΠΈ ΠΏΡΠΎΠΈΠ·Π²ΠΎΠ΄ΡΡΠ²Π°
Critical dimensions for random walks on random-walk chains
The probability distribution of random walks on linear structures generated
by random walks in -dimensional space, , is analytically studied
for the case . It is shown to obey the scaling form
, where is
the density of the chain. Expanding in powers of , we find that
there exists an infinite hierarchy of critical dimensions, ,
each one characterized by a logarithmic correction in . Namely, for
, ; for ,
; for , ; for , ; for , , {\it etc.\/} In particular, for
, this implies that the temporal dependence of the probability density of
being close to the origin .Comment: LATeX, 10 pages, no figures submitted for publication in PR
Reconstruction of protein structures from a vectorial representation
We show that the contact map of the native structure of globular proteins can
be reconstructed starting from the sole knowledge of the contact map's
principal eigenvector, and present an exact algorithm for this purpose. Our
algorithm yields a unique contact map for all 221 globular structures of
PDBselect25 of length . We also show that the reconstructed contact
maps allow in turn for the accurate reconstruction of the three-dimensional
structure. These results indicate that the reduced vectorial representation
provided by the principal eigenvector of the contact map is equivalent to the
protein structure itself. This representation is expected to provide a useful
tool in bioinformatics algorithms for protein structure comparison and
alignment, as well as a promising intermediate step towards protein structure
prediction.Comment: 4 pages, 1 figur
Josephson junction between anisotropic superconductors
The sin-Gordon equation for Josephson junctions with arbitrary misaligned
anisotropic banks is derived. As an application, the problem of Josephson
vortices at twin planes of a YBCO-like material is considered. It is shown that
for an arbitrary orientation of these vortices relative to the crystal axes of
the banks, the junctions should experience a mechanical torque which is
evaluated. This torque and its angular dependence may, in principle, be
measured in small fields, since the flux penetration into twinned crystals
begins with nucleation of Josephson vortices at twin planes.Comment: 6 page
Emergence of Spacetime
Starting from a background Zero Point Field (or Dark Energy) we show how an
array of oscillators at the Planck scale leads to the formation of elementary
particles and spacetime and also to a cosmology consistent with latest
observations.Comment: Latex, 39 page
Use of Assessment Indicators to Forecast Market Promotion of Products
During recent years the trend to tighten competitiveness has been increasing globally almost in all industries, although before then it was absent in many countries and economic sectors. This article touches upon the main issues regarding the competitiveness of enriched curd products with prebiotic substances. On the basis of a consumer survey, the calculation of advantageous indicators was performed. According to the results of the ranking of quality indicators, the following maximum values were accepted: taste and smell, form and consistency, titratable acidity, amino acid composition, and vitamin and mineral composition. A comparative analysis of consumer qualities of curd products is given. According to the results of the assessment of the quality of curd products, it can be concluded that competitive advantage belongs to a curd product enriched with cedar oil cake, lactulose syrup and whey proteins. This is followed by the curd product enriched with cedar oil cake and lactulose syrup, and then the integral indicator in the curd sample enriched with cedar oil cake. The integral indicators of curd cream and curd cheese have low values: 0.16 and 0.145, respectively. Thus, the developed curd products enriched with prebiotic substances will be in demand in the modern market of curd products.
Keywords: competitiveness, complex quality indicator, curd products, cedar oil cake, whey protein, lactulos
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