On the possibility of remote detection of conductive layers

A two-dimensional medium is considered in which the fields are described by the Helmholtz equation. The linearized formulation of the problem of restoring the parameters of the medium (the inverse problem for the Helmholtz equation) is studied. The conditions for the uniqueness of detection of thin conducting layers are established. Examples are given of the multivaluedness of the solution of the inverse problem in information, which was initially thought to be even redundant for an unambiguous solution. &nbsp

Invariance of ϕ4\phi^4 measure under nonlinear wave and Schr\"odinger equations on the plane

We show probabilistic existence and uniqueness for the Wick-ordered cubic nonlinear wave equation in a weighted Besov space over $\mathbb R^2$. To achieve this, we show that a weak limit of $\phi^4$ measures on increasing tori is invariant under the equation. We review and slightly simplify the periodic theory and the construction of the weak limit measure, and then use finite speed of propagation to reduce the infinite-volume case to the previous setup. Our argument also gives a weak (Albeverio--Cruzeiro) invariance result on the nonlinear Schr\"odinger equation in the same setting.Comment: 50 pages. Major reorganization of Sections 1 and 3, revision and improvements throughou

The Phi(4)(3) measure via Girsanov's theorem

We construct the Phi(4)(3) measure on a periodic three dimensional box as an absolutely continuous perturbation of a random translation of the Gaussian free field. The shifted measure is constructed via Girsanov's theorem and the relevant filtration is the one generated by a scale parameter. As a byproduct we give a self-contained proof that the Phi(4)(3) measure is singular wrt. the Gaussian free field.Peer reviewe

On the variational method for Euclidean quantum fields in infinite volume

We investigate the infinite volume limit of the variational description of Euclidean quantum fields introduced in a previous work. Focussing on two dimensional theories for simplicity, we prove in details how to use the variational approach to obtain tightness of $\varphi^4_2$ without cutoffs and a corresponding large deviation principle for any infinite volume limit. Any infinite volume measure is described via a forward--backwards stochastic differential equation in weak form (wFBSDE). Similar considerations apply to more general $P (\varphi)_2$ theories. We consider also the $\exp (\beta \varphi)_2$ model for $\beta^2 < 8 \pi$ (the so called full $L^1$ regime) and prove uniqueness of the infinite volume limit and a variational characterization of the unique infinite volume measure. The corresponding characterization for $P (\varphi)_2$ theories is lacking due to the difficulty of studying the stability of the wFBSDE against local perturbations.Comment: 39 pages, some corrections and remarks on the FBSDE formulatio

The Method of Prime Costs Determination of the Model Row Goods

The concept of the model row goods is introduced. These are the&nbsp;interchangeable goods differing by quality and price. Cognacs of various vintage years&nbsp;produced on one cognac factory are a typical example of such goods. For the indicated&nbsp;kind of the goods the method of the cost price determination of the goods of competitors is worked out and realized. The initial information for determination is the data on the&nbsp;prices of the goods and sales volumes

Improving the thermostability of horseradish peroxidase by incorporating into water-immiscible coacervates

Looking for novel matrix materials for encapsulation of enzymes based on water immiscible coacervates prepared by reaction of negatively charged hyaluronic acid and a positively charged recombinant mussel adhesive protein containing tyrosine residues was the subject of the investigation of this work. The results of experimental study of the thermostability of horseradish peroxidase (HRP) by means its encapsulation in these coacervates at temperature from 30 to 95oC is presented in this paper. The Michaelis-Menten equation was applied to analyze of the enzymatic activity of HRP. The kinetic parameters were interpreted using a Lineweaver-Burk plot. According to the data obtained, Michaelis-Menten parameters, KM and KCat , interpreted from the Lineweaver- Burk plots, were 0.271 mM and 2265 s-1 for the free HRP and 0.325 mM and 2158 s-1 for the rMAP/HA coacervate, containing HRP, respectively, which indicate that the enzyme did not lose its activity during the coacervate formation. It was founded that the free enzyme began to lose activity above 40oC, while the encapsulated HRP remained stable to 85oC. The encapsulated HRP lost only 18% and 25% of activity at temperature of 90 and 95oC, respectively, while as free HRP loses all its initial activity, although they show similar activity at room temperature.Keywords: encapsulation, hyaluronic acid, coacervate, recombinant mussel adhesive protei

Аналоговые формы гражданского общества (на примере стран исламского ареала)

The article deals with the analogue forms of civil society in the Islamic countries of the South. The author analyzes the formation and development of the civil society in this region of the world, its specifics and peculiarities. The author also shows that burgeoning civil society models of non-western area have their own specific features, which are determined by a unique way of civilizational development and by significant impact of the religious factor. The present research brings up a methodological novation – an analogous civil society. According to this novation, the developing political system (which takes part in civilizational competition with other systems and tries to use their historical experience and accumulated resources explicitly, for example, by attracting ideas, technologies, investments, or implicitly – by creating the same resources through modernization and social mobilization) does not imply an organic link between ideologically reflected meaning of this system’s existence, the forms of such existence, and the main institutions’ functionality. Moreover, this smoothness is not very important and desirable for the analogue system or its components. The meaning of such system’s existence is using the forms, principles, mechanisms, elaborated through historical development of social and political systems for their own specific purposes, for the sake of diametrically opposed goals that sometimes are not very detailed

Multiscale coupling and the maximum of P(ϕ)2\mathcal{P}(\phi)_2 models on the torus

We establish a coupling between the $\mathcal{P}(\phi)_2$ measure and the Gaussian free field on the two-dimensional unit torus at all spatial scales, quantified by probabilistic regularity estimates on the difference field. Our result includes the well-studied $\phi^4_2$ measure. The proof uses an exact correspondence between the Polchinski renormalisation group approach, which is used to define the coupling, and the Bou\'e-Dupuis stochastic control representation for $\mathcal{P}(\phi)_2$. More precisely, we show that the difference field is obtained from a specific minimiser of the variational problem. This allows to transfer regularity estimates for the small-scales of minimisers, obtained using discrete harmonic analysis tools, to the difference field. As an application of the coupling, we prove that the maximum of the $\mathcal{P}(\phi)_2$ field on the discretised torus with mesh-size $\epsilon > 0$ converges in distribution to a randomly shifted Gumbel distribution as $\epsilon \rightarrow 0$.Comment: 45 page