On the Parabolic and Hyperbolic Liouville Equations

We study the two-dimensional stochastic nonlinear heat equation (SNLH) and stochastic damped nonlinear wave equation (SdNLW) with an exponential nonlinearity $$\lambda \beta e^{\beta u }$$ λ β e β u , forced by an additive space-time white noise. (i) We first study SNLH for general $$\lambda \in {\mathbb {R}}$$ λ ∈ R . By establishing higher moment bounds of the relevant Gaussian multiplicative chaos and exploiting the positivity of the Gaussian multiplicative chaos, we prove local well-posedness of SNLH for the range $$0< \beta ^2 < \frac{8 \pi }{3 + 2 \sqrt{2}} \simeq 1.37 \pi $$ 0 < β 2 < 8 π 3 + 2 2 ≃ 1.37 π . Our argument yields stability under the noise perturbation, thus improving Garban’s local well-posedness result (2020). (ii) In the defocusing case $$\lambda >0$$ λ > 0 , we exploit a certain sign-definite structure in the equation and the positivity of the Gaussian multiplicative chaos. This allows us to prove global well-posedness of SNLH for the range: $$0< \beta ^2 < 4\pi $$ 0 < β 2 < 4 π . (iii) As for SdNLW in the defocusing case $$\lambda > 0$$ λ > 0 , we go beyond the Da Prato-Debussche argument and introduce a decomposition of the nonlinear component, allowing us to recover a sign-definite structure for a rough part of the unknown, while the other part enjoys a stronger smoothing property. As a result, we reduce SdNLW into a system of equations (as in the paracontrolled approach for the dynamical $$\Phi ^4_3$$ Φ 3 4 -model) and prove local well-posedness of SdNLW for the range: $$0< \beta ^2 < \frac{32 - 16\sqrt{3}}{5}\pi \simeq 0.86\pi $$ 0 < β 2 < 32 - 16 3 5 π ≃ 0.86 π . This result (translated to the context of random data well-posedness for the deterministic nonlinear wave equation with an exponential nonlinearity) solves an open question posed by Sun and Tzvetkov (2020). (iv) When $$\lambda > 0$$ λ > 0 , these models formally preserve the associated Gibbs measures with the exponential nonlinearity. Under the same assumption on $$\beta $$ β as in (ii) and (iii) above, we prove almost sure global well-posedness (in particular for SdNLW) and invariance of the Gibbs measures in both the parabolic and hyperbolic settings. (v) In Appendix, we present an argument for proving local well-posedness of SNLH for general $$\lambda \in {\mathbb {R}}$$ λ ∈ R without using the positivity of the Gaussian multiplicative chaos. This proves local well-posedness of SNLH for the range $$0< \beta ^2 < \frac{4}{3} \pi \simeq 1.33 \pi $$ 0 < β 2 < 4 3 π ≃ 1.33 π , slightly smaller than that in (i), but provides Lipschitz continuity of the solution map in initial data as well as the noise.

Soft-collinear effective theory: BRST formulation

We provide a BRST formalism for the soft-collinear effective theory describing interactions of soft and collinear degrees of freedom in the presence of a hard interaction. In particular, we develop a BRST symmetry transformation for SCET theory. We further generalize the BRST formulation by making the transformation parameter field dependent. This establishes a mapping between several SCET actions consistently when defined in different gauge conditions. In fact, a definite structure of gauge-fixed actions corresponding to any particular gauge condition can be generated for SCET theory using our formulation.

Tari Dalam Seni Pertunjukan Angklung Badud di Desa Parakan Honje Kota Tasikmalaya

The performing art of Badud Angklung in Parakan Honje Village, Indihiang District, Tasikmalaya City is a typical art from the city of Tasikmalaya by incorporating the results of its unique skills, namely umbrellas and geulis kelom. The problems raised are: 1) What is the form of presentation of Badud Angklung Performing Arts in Parakan Honje Village, Indihiang District, Tasikmalaya City ?; 2) How is the presentation of dance in the Badud Angklung Performing Arts in Parakan Honje Village, Indihiang District, Tasikmalaya City ?; 3) How are the clothes and make-up in the performing arts of Badud Angklung in Parakan Honje Village, Indihiang District, Tasikmalaya City? This research uses the theory of performance studies and descriptive analysis methods with a qualitative approach to describe and explain natural problems related to the performing arts of Badud Angklung and to analyze the form of presentation, the form of presentation of dance and make-up and clothing in the Angklung Badud performance art. It can be concluded that the performing art of Badud Angklung is in the form of parades with the concept of being reproduced, namely adding to the dance and the people who participate in this art, when the procession takes place the movements performed do not have a definite structure while when they form a formation the dance has a definite structure. Namely the geulis umbrella dance and the Badud angklung dance. The male players' make-up is an everyday make-up and the clothes are red and blue and iket to make the traditional elements more visible. Female dancers wear corrective make-up and dress in yellow and use geulis clamps and umbrellas as an identity that this art originates from Tasikmalaya.

Name-strategies and antropoiesis discourse in the history of philosophy

Onomapoiesis strategies actualize the distinctive sphere of human practice, which is a direct continuation of autopoiesis and anthropoiesis. They atomize and ontologize the Self by restricting it to definite structure-morphologic clusters of language expressions, such as personal name and pronoun. As a result, we have two completely different tactics: naming tactics and pronoun tactics, or ego-strategies. These practices refer to diverse complexes and can’t be considered within one species, each of them constitutes the autonomous entity. Any self-naming, self-calling, and indication through the name or pronoun, correlates with the innate eager and desire of a person to express himself, the world, and other(s). Thus, the anthropology of naming turns out to be the part of philosophical discourse, implicitly passing through the entire history of thought. Primarily, the philosophy of Stoics belongs to this kind of boundary marks, within the framework of which the distinction between the name and the pronoun was made for the first time. Plus, the discovery of deixis belongs to them. In the context of the modern era of philosophy, the doctrine of Rene Descartes is a kind of counterpoint when the Self, the Ego, first reveals itself to consciousness. Further, there is a fission inside the indicated complexes: I and not-I, My and not-My, I and You, We and They, I and the Other, I and Others manifest themselves inside the pronoun practices of naming. Their contents and meanings become the subject of philosophy and linguistic, as well as interdisciplinary studies. There are two conceptually framed strategies within one complex, which illustrates the praxeological character of the study: the Heideggerian Dasein and the polyphonic Ego presented by Bakhtin M.M. The first one unfolds as a monologue and first-person speech; the latter in turn, as a dialog, which expresses the subject’s being as a complicity in the polyphony of voices of the Other(s).

Cast iron rolls

The manufacturing process of the rolling rolls, as well as the quality of materials used in casting them, can have an important influence upon the quality and the safety of the exploitation. Our approaches to the issue of quality assurance of the rolling rolls, from the viewpoint of the quality of materials that are featured, can cause duration and safety in the rolling exploitation. This research is required because of the numerous flaws that cause rejection, since the phase of melting of these irons is intended to cast rolls. According to the industrial analysis in the cast iron rolls foundries, the results show that one of the main rejection categories is due to the inadequate hardness of the rolls. One of the parameters that will determine the cast iron’s structure is the chemical composition, and this factor could assure the exploitation properties of each roll in all the stands of rolling mill. In this sense, the paper presents an overview of industrial and laboratory research regarding the assurance of the chemical composition of the irons (with nodular graphite) destined for the half–hard rolls casting, and tries to draw some remarks upon the proper correlations of these irons. This study analyses iron rolls cast in combined moulds (iron chill, for the barrel and moulding sand, for the necks of rolls) and includes charges of rolls from half–hard classes, with definite structure and nodular graphite, obtained in simplex cast processes. It presents, in graphical form, the influence of the chemical composition of these irons on the hardness, measured on the barrel. The proper solution is determined through some mathematical restrictions to the input data that the mathematical modelling is initiated with. It will be determined through regression equations, which describe the mathematical dependency between the hardness and the elements of chemical composition – the basic elements (Carbon [C], Manganese [Mn] and Silicon [Si]), the particulate elements (Sulphur [S], Phosphorus [P] and Magnesium [Mg]) and the main alloying elements (Nickel [Ni], Molybdenum [Mo] and Chrome [Cr]). The main results and the graphical addenda are presented.

Discrete Cosine Transform Matrix Based SLM Algorithm for OFDM with Diminished PAPR for M-PSK over Different Subcarriers

Orthogonal frequency division multiplexing (OFDM) is the highly spectrally well-organized method that has the difficulty of excessive peak power to average power ratio (PAPR), which ultimately imposes constraints on the high-power amplifier. Many practices have been projected to lessen PAPR of the OFDM systems. Amongst all the practices, the selected mapping (SLM) method has drawn more attention because of distortion-less behaviour. This technique uses unique phase sequences. It has been learnt that phase formation for SLM is very tedious. In the proposed work, the SLM method has been used, but phase arrangement formation is based on the usage of discrete cosine transform (DCT) matrix. In this proposed work, discrete cosine transform matrix has been chosen based on the requirement of optimization so that the arrangement with lowest PAPR can be nominated for the transmission. MATLAB simulation depicts that the remarkable gain is achieved as compared with the existing technique. In the proposed work, scheming of phase sequences are very informal due to the use of a DCT matrix which has a definite structure and can be generated at the receiver side with the help of side information of the phases and communicated from the transmitter to the receiver.

Ovarian characteristics in the fetal period: topographic and morphometric parallels

Defects of the urinary system take the 3rd place by their occurrence including 6% of developmental defects of the female reproductive organs. Therefore modern studies in the field of perinatal anatomy are of a special importance. Objective of the study was to determine age peculiarities in the structure and topography of the fetal ovaries as well as similar and different tendencies in changes of the ovarian morphological parameters of the two groups of fetuses, remote in time. The study was conducted in the two groups of human fetuses, 4-10 months of development, 161.0-500.0 mm of the parietal-calcaneal length. The first group consisting of 35 specimens divided into 7 subgroups according to the month of development (4, 5, 6, 7, 8, 9 and 10), was formed with fetuses died during 2017-2019 years. The second group included specimens of fetuses collected during 1970-1990. The obtained results were statistically processed in the licensed statistical package “Statistica 6.0”. The character of distribution for every obtained variation lines, mean values for every sign, standard quadratic deviation, percentile scope of the parameters were evaluated. Reliability of differences in the indices between independent quantitative values was determined by means of Mann-Whitney U-criterion. The conducted study determined that the ascending position of the ovaries in the early fetuses can be considered normal for the given age group, though the topography is indicative of developmental retardation at the late stages of perinatal development. The length of the ovary in both groups increases gradually from the 4th to the 10th month with a certain delay during the 6th month. It might be associated with intensified growth of its parenchyma, and intensive increase of its width and length respectively. The majority of the ovarian parameters of 9-10 month fetuses do not differ reliably, which is indicative of a complete development of the ovarian definite structure at the 9th month of the intrauterine development. Comparison of the parameters of the two groups of fetal specimens, remote in time, is indicative of the fact that in the majority of the parameters they do not differ. Although in modern studies the length of the right ovary in 8-month fetuses, and the length of the left ovary in 7-month fetuses is shorter than that of the archival specimens. Similarly the width of the left ovary in 4-month fetuses appears to be reliably shorter than that of the archival specimens. The thickness of the right ovary of 7 and 10-month modern fetuses is reliably less than that of the appropriate groups of the archival specimens. The thickness of the left ovary of modern fetuses is reliably less than that of the archival specimens during the 10th month. Therefore, a reliable difference was found only in 2 pairs of the parameters included in 42 pairs of the examined morphometric parameters of both groups. It is indicative of inconsiderable changes of these parameters during the period of 27-49 years.

Networks Describing Dynamical Systems

We consider systems of ordinary differential equations that arise in the theory of gene regulatory networks. These systems can be of arbitrary size but of definite structure that depends on the choice of regulatory matrices. Attractors play the decisive role in behaviour of elements of such systems. We study the structure of simple attractors that consist of a number of critical points for several choices of regulatory matrices.

FETAL ANATOMY OF THE ILEOCECAL SEGMENT

A number of publications in modern Ukrainian and foreign publications deal with investiga-tions of the anatomy of the ileocecal segment. The data of the majority of authors are fragmentary and incomplete, and mostly deal with investigations of anatomy of a definite form of the ileocecal segment or embryonic formation of iliac papilla. The literature does not contain a common opinion concerning the dynamics of formation of the iliac papilla, variants of its anatomy, mechanism of its sphincter function. The study is conducted on 125 dead fetuses and complexes of organs of fetuses and human newborns without evident macroscopic signs of deviation from a normal structure of the digestive tract. Morphogenesis of the sphincter-valve mechanism of the ileocecal transition is of invagination type accompanied by temporary closing of the junction between the small and large intestines, and as a result, dilation of the terminal portion of the ileum, diameter of which on the 7th month of develop-ment (6,0±0,4 mm) prevails over the diameter of the proximal segment of the colon (5,7±0,8 mm). Formation of a definite structure of the components of the ileocecal segment and variants of its struc-ture is affected by a syntopogenous influence of the right kidney, the processes of colon fixation to the posterior abdominal wall, and degree of filling the intestine with meconium.