Lp Type Research Articles

On the Unique Continuation Property for a Coupled System of Third-order Nonlinear Schrodinger Equations

In this paper, we study the unique continuation properties for a coupled system of third-order nonlinear Schrodinger equations and show the Carleman estimates of L2 and Lp (p > 2) types, as well as exponential decay properties of the solutions. As a consequence we obtain that if (\(\mathit{u}\), \(\mathit{w}\)) = (\(\mathit{u}\)(\(\mathit{x}\), \(\mathit{t}\)), \(\mathit{w}\)(\(\mathit{x}\), \(\mathit{t}\))) is a suffciently smooth solution of the system such that there exists \(\mathit{l}\) \(\in\) \(\mathbb{R}\) with supp \(\mathit{u}\)(.,tj) \(\subseteq\)(\(\mathit{l}\), \(\infty\)) (\(\mathit{or}\)(-\(\infty\), \(\mathit{l}\))) and supp \(\mathit{w}\)(.,tj) \(\subseteq\)(\(\mathit{l}\), \(\infty\)) (\(\mathit{or}\)(-\(\infty\), \(\mathit{l}\))), for \(\mathit{j}\) = 1,2 (t1 \(\neq\) t2), then \(\mathit{u}\) \(\equiv\) 0 and \(\mathit{w}\) \(\equiv\) 0.

Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization

Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way to align with a target 3D shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and partial overlap) and high degrees of freedom. Existing methods typically adopt the lp type robust norm to measure the alignment error and regularize the smoothness of deformation, and use a proximal algorithm to solve the resulting non-smooth optimization problem. However, the slow convergence of such algorithms limits their wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust norm for alignment and regularization, which can effectively handle outliers and partial overlaps. The problem is solved using the majorization-minimization algorithm, which reduces each iteration to a convex quadratic problem with a closed-form solution. We further apply Anderson acceleration to speed up the convergence of the solver, enabling the solver to run efficiently on devices with limited compute capability. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlaps, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/yaoyx689/AMM_NRR.

Propagation of chaos for stochastic particle systems with singular mean-field interaction of Lq−Lp type

Propagation of chaos for stochastic particle systems with singular mean-field interaction of Lq−Lp type

Neural network operators of fuzzy n-cell number valued functions and multidimensional fuzzy inference system

In this paper, we introduce a novel family of neural network operators of fuzzy n-cell number valued functions, activated by a collection of multivariate sigmoidal functions. We give some special examples of these activation functions with graphs and present some illustrative examples to demonstrate the approximation performance of these operators. Moreover, we propose a multidimensional fuzzy inference system including neural network operators of fuzzy n-cell number valued functions for the symptom-based diagnosis of Covid-19 disease. Finally, we give some approximation results using an Lp type metric of fuzzy n-cell numbers and examine the rate of convergence for the operators by means of fuzzy Lp modulus of continuity.

Vectorial Prabhakar Hardy Type Generalized Fractional Inequalities under Convexity

We present a detailed great variety of Hardy type fractional inequalities under convexity and Lp norm in the setting of generalized Prabhakar and Hilfer fractional calculi of left and right integrals and derivatives. The radial multivariate case of the above over a spherical shell is developed in detail to all directions. Many inequalities are of vectorial splitting rational Lp type or of separating rational Lp type, others involve ratios of functions and of fractional integral operators.

Novel Tee-Shaped Topology Theory of Low- and High-Pass NGD Double-Type Function

Recent investigation reports that certain electronic circuits operate with the unfamiliar negative group delay (NGD) function. It is fundamentally stated that the NGD circuits can be classified in different types. For example, we have the simplest ones as LP and HP NGD circuit types. So far, all the NGD studies are focused on simple type function. In step up of the research about the NGD electronic circuit engineering, this paper develops an original theory of electronic circuit topology operating with double NGD-type behavior. The study consists in the theorization of three-port circuit simultaneously generating LP and HP NGD function types. The proposed three-port innovative circuit under study is innovatively composed of resistive-capacitive (RC) network of Tee-shaped topology. Moreover, the LP and HP double-NGD circuit is a first order cell which does not contain any inductive component. The LP and HP NGD analyses of the Tee-topology is based on the 3-D S-matrix modelling. Analytical investigation based on classical circuit theory is elaborated to determine the S-matrix model from the equivalent admittance matrix. The identification of the double-NGD function is established from the LP- and HP-NGD canonical forms. Hence, the specific double-NGD characteristics are defined in function of the R and C elements constituting the three-port topology. To validate the developed double-NGD theory, a proof-of-concept (PoC) of SMD lumped component-based three-port circuit is designed, simulated, fabricated and tested. The calculated, simulated and measured results from the three-port circuit PoC prototype in very good agreement confirm the double-NGD behavior. The proposed innovative NGD three-port circuit design is useful in the future for the synchronization of signals propagating through multi-way communication system.

One-year clinical results of isolated coronary artery bypass surgery due to type of lesion and LP(A) level

One-year clinical results of isolated coronary artery bypass surgery due to type of lesion and LP(A) level

Local and global well-posedness, and [formula omitted]-decay estimates for 1D nonlinear Schrödinger equations with Cauchy data in Lp

An Lp-theory of local and global solutions for the one dimensional nonlinear Schrödinger equations with pure power like nonlinearities is developed. Firstly, twisted local well-posedness results in scaling subcritical Lp-spaces are established for p<2. This extends Zhou's earlier results for the gauge-invariant cubic NLS equation. Secondly, by a similar functional framework, the global well-posedness for small data in critical Lp-spaces is proved, and as an immediate consequence, Lp′-Lp type decay estimates for the global solutions are derived, which are well known for the global solutions to the corresponding linear Schrödinger equation. Finally, global well-posedness results for gauge-invariant equations with large Lp-data are proved, which improve earlier existence results, and from which it is shown that the global solution u has a smoothing effect in terms of spatial integrability at any large time. Various Strichartz type inequalities in the Lp-framework including linear weighted estimates and bi-linear estimates for Duhamel type operators play a central role in proving the main results.

Novel fixed point approach to Atangana-Baleanu fractional and [formula omitted]-Fredholm integral equations

In this article, we introduce an extended F-metric and proved related fixed point results. Subsequently, we mainly focus on(a): Solution for the Atangana-Baleanu fractional integral of order ∝ of a function f(t)It∝sABζ(t)=1-∝B(∝)ζ(t)+∝B(∝)Γ(∝)∫0tζ(ρ)(t-ρ)∝-1dρ;where 0<∝⩽1,0<t<s and it is worthy to mention B(0) and B(1) are equal to 1.(b): LP type solution (1<p<∞) for the linear Fredholm integral equation of the second kind▪where ▪

P4485The number of lipoprotein(a) kringle IV-type 2 repeats is associated with the osteogenic profile of aortic valvular interstitial cells induced by plasma from patients with calcific aortic stenosis

Abstract Background Considerable progresses have been made in the invasive treatment of calcific aortic stenosis (AS), but there is still no pharmacological treatment available because the exact mechanism leading to the initiation of valvular calcification remains unknown. An increasing number of evidences, including large-scale genetic studies, have linked Lipoprotein(a) (Lp(a)) to AS but its pathogenic role in the osteoblastic transition of valvular interstitial cells (VIC) has remained undeciphered. Objective We sought to study the mechanistic link between the transition of VICs towards an osteoblastic phenotype leading to intraleaflet calcium deposition and the type of Lp(a) isoform, defined by the number of kringle IV-type 2 (KIV 2) repeats, in the plasma of patients with AS compared with healthy controls. Methods VICs isolated from healthy aortic valves were cultured in the presence of plasma samples deriving from 100 patients with severe AS included in the prospective cohort GENERAC and 50 matched control patients exempt from any aortic valve disease. We evaluated the number of Lp(a) KIV 2 repeats of each plasma preparation by liquid chromatography-mass spectrometry. The phenotypic changes of VICs towards an osteoblastic phenotype were assessed by immunofluorescence microscopy (osteocalcin expression) and Alizarin red staining (calcium deposition). Results Incubation of VICs with the plasma of AS patients triggered their transformation towards an osteoblastic phenotype, evidenced by the production of osteocalcin, and calcium deposition. There was no association between the plasma levels of Lp(a) and the extent of calcium deposition in the study population. However, a negative and significant correlation was found between calcium deposition and the number of KIV-2 repeats in the Lp(a) of the different plasma preparations (r=−0.20, p=0.038). A direct, causal role of Lp(a) isoforms containing a low number of KIV-2 repeats (5 to 6) in the transition of VICs towards an osteoblastic phenotype was supported by experiments performed with preparations of these isoforms, isolated from the plasma of blood donors. Conclusion A low number of KIV–2 repeats in plasma Lp(a) triggers the acquisition of an osteoblastic phenotype by VICs. The isoform, rather than the concentration of Lp(a) may play a pathogenic role in AS. Determining the number of KIV-2 repeats in the Lp(a) of patients may allow to identify subgroups of patients with an increased risk of developing AS. Acknowledgement/Funding ANR-16-RHUS-0003_STOP-AS. PHRC National 2005 and 2010, and PHRC regional 2007.

The Hájek-Rényi-Chow maximal inequality and a strong law of large numbers in Riesz spaces

In this paper we generalize the Hájek-Rényi-Chow maximal inequality for submartingales to Lp type Riesz spaces with conditional expectation operators. As applications we obtain a submartingale convergence theorem and a strong law of large numbers in Riesz spaces. Along the way we develop a Riesz space variant of the Clarkson's inequality for 1≤p≤2.

Properties of fuzzy transform obtained from Lp minimization and a connection with Zadeh’s extension principle

In 2006 Perfilieva proved that the components Fk of the fuzzy transform are actually minimizers of certain weighted L2 type distances, obtained from a fuzzy partition. Inspired by this property, we consider and analyze the properties of a fuzzy transform when the components Fk are obtained as minimizers with respect to weighted Lp type distances, where p ≥ 1. In this way we can generate new approximation operators based on the fuzzy transform method. For these operators we obtain good rates of uniform convergence and what is more, they satisfy all the properties required for an effective approximation operator, such as additivity and homogeneity. If we consider the extended fuzzy transform and inverse fuzzy transform, respectively, in this setting of Lp type distances, then we get some nice supplementary properties like monotonicity of the operator and preservation of monotone functions. Finally, we consider fuzzy-valued versions of the L1 and L2 type fuzzy transforms, proposed recently as quantile and expectile smoothing tools, and we prove that the L1 type fuzzy-valued transform of a continuous monotonic function f coincides with the Zadeh’s fuzzy extension fEP evaluated at suitable fuzzy numbers, obtained from the basic functions of the used fuzzy partition.

Nonstationary radiation transfer through a multilayered medium with reflection and refraction conditions

We consider an initial‐boundary value problem for the radiation transfer equation with reflection and refraction conditions describing a nonstationary process of the radiation transfer in multilayered semitransparent for radiation medium, consisting of m parallel vertical layers. We establish the existence and uniqueness of a solution for the problem with data from the spaces of Lp type, 1 ≤ p ≤ ∞. We also obtain a priori estimates for the solution and prove an exponential stabilization of the solution as T→∞.

Formation Conditions of Basic Granulites and High-Alumina Gneiss of the Baikal–Muya Belt (Northern Baikal Area)

The Kichera zone of the Baikal–Muya Belt consists of alternating tectonic plates with rocks of different metamorphic facies. Garnet–cordierite–sillimanite gneiss from the tectonic fragment in granite–gneiss of the Baikal massif with an age of 755 ± 15 Ma from the Goremyka plate and two-pyroxene schist of the granulite complex with an age of 617 ± 5 Ma from the Boguchan plate were studied. Thermobarometric studies of these key metamorphic rocks were carried out using the avPT (THERMOCALC) and TWEEQU (TWQ 2.01) methods. The P–T parameters estimated for the cordierite⎯sillimanite gneiss of the Goremyka plate correspond to the boundary between the amphibolite and granulite facies. Granulites of the Boguchan plate belong to the HT–LP type. Exhumation of metamorphic rocks could be caused by extension upon the evolution of the Late Baikal rifting.

Local Tb theorem with L 2 testing conditions and general measures: square functions

Local Tb theorems with L p type testing conditions, which are not scale invariant, have been studied widely in the case of the Lebesgue measure. In the non-homogeneous world local Tb theorems have only been proved assuming scale invariant (L ∞ or BMO) testing conditions. In this paper, for the first time, we overcome these obstacles in the non-homogeneous world, and prove a nonhomogeneous local Tb theorem with L 2 type testing conditions. This paper is in the setting of the vertical and conical square functions defined using general measures and kernels. On the technique side, we demonstrate a trick of inserting Calderon–Zygmund stopping data of a fixed function into the construction of the twisted martingale difference operators. This built-in control of averages is an alternative to Carleson embedding.

옥외영상의 개선된 차량번호판 인식기술

일반적으로 옥외영상에서의 자동차 번호판 인식은 인위적인 환경에서와는 다르게 기하학적으로 왜곡되어 있을 뿐만 아니라 조명 변화도 크기 때문에 단순환 문제가 아니다. 본 논문에서는 일반 CCTV 카메라로 옥외에서 촬영된 영상에서 자동차 번호판 인식을 위한 개선된 기술들을 제안한다. 먼저 다양한 특징을 상보적으로 사용하는 직렬구조의 다단계 Adaboost 검출기를 제안한다. 제안하는 검출기는 MB-LBP 및 Haar-like 특징을 사용하는 Adaboost 구조를 직렬로 연결하여 번호판 검출의 검출성능을 향상시켰다. 또한 검출된 번호판의 기하학적 왜곡을 보정하고 번호판의 타입을 먼저 결정하여 영상처리를 용이하게 하는 방법을 제안한다. 이런 방법은 그래이 변환, 문자/숫자 분리, 분리된 영상의 영상처리 등에서 사전지식 없이 전체 번호판 영상을 이용하는 경우보다 효율적이다. 본 논문에서 DBN(Deep Belief Network)를 문자/숫자 인식기로 사용하여 영상처리과정에서 기인한 획 손실이나 기울어짐 같은 기하학적인 왜곡에서도 강건한 인식률을 달성하였다. In general LPR(License Plate Recognition) in outdoor image is not so simple differently from in the image captured from manmade environment, because of geometric shape distortion and large illumination changes. this paper proposes three techniques for LPR in outdoor images captured from CCTV. At first, a serially connected multi-stage Adaboost LP detector is proposed, in which different complementary features are used. In the proposed detector the performance is increased by the Haar-like Adaboost LP detector consecutively connected to the MB-LBP based one in serial manner. In addition the technique is proposed that makes image processing easy by the prior determination of LP type, after correction of geometric distortion of LP image. The technique is more efficient than the processing the whole LP image without knowledge of LP type in that we can take the appropriate color to gray conversion, accurate location for separation of text/numeric character sub-images, and proper parameter selection for image processing. In the proposed technique we use DBN(Deep Belief Network) to achieve a robust character recognition against stroke loss and geometric distortion like slant due to the incomplete image processing.

Factors affecting the lactation curves of intensively managed sheep based on a clustering approach

This study investigated factors affecting milk production and lactation curves from complete lactations of Lacaune dairy sheep. Animals were part of a single flock under intensive management and were milked twice daily starting at lambing. The results of the analyses of 7788 complete lactations showed an average total milk yield of 434±183l from lactations 234±63d long, with an average lambing interval of 302±65d. A Pollott additive mathematical model was used to estimate complete lactation curves. Clustering analysis identified four lactation types among Lacaune dairy sheep differing mainly in productivity i.e. milk yield per lactation (MY) and length of lactation (DIM). The so-called SL type involved short, less productive lactations (n=2137; 27·4%; MY=222±75·5l and DIM=182±52·9d). The SN type involved short lactations of normal productivity (n=2039; 26·2%; MY=396±73·7l and DIM=205±33·1d). The LP type involved long and productive lactations (n=2169; 27·9%; MY=487±70·5l and DIM=265±40·7d), while the LVP type included long and extremely productive lactations (n=1443; 18·5%; MY=694±114·0l and DIM=295±54·7d). Sheep showing the best lactation curves were usually younger than other sheep, and they had higher yield during the previous lactation, a shorter previous dry period (55±50·4 for LP and 61±55·0d for LVP types) and longer lambing intervals. In addition, they tended to be born in September and to lamb in March, October and December. Sheep were remarkably stable in their lactation curve behaviour: the curve type observed for the first lactation was highly likely to persist in subsequent lactations (P<0·0001). These results suggest that farmers can use the shape of the first lactation curve to guide their selection of ewes for breeding and retention on the farm, thereby improving flock productivity.

A study on lichen planus in children

Introduction: Lichen planus is considered to be rare in children. However, it does not appear to be uncommon in Indian subcontinent. Aims: The study was undertaken to analyse the clinical profile of childhood lichen planus. Material and Methods: We selected 30 children with LP for the study. The children selected were below the age of 14 years of age. Results and Discussion: In our study, it was seen that that the maximum onset of disease was between 5-9 years of age and mean age of children with LP was 6.8 years. The commonest type of LP in children was classical LP seen in 60% children, followed by actinic LP in 20% children. LP hypertrophicus and linear LP were seen in 10% patients each. Nail changes were seen in 10% patients.

SOME CLASS OF OPERATOR IDEALS

In 1975, Rhoades (9) generalized the classes of, operators of lp type and operators of Cesaro type by introducing an arbitrary infinite matrix A = (ank) using approximation numbers of a bounded linear operator. In the same paper Rhoades has proved that for each fixed matrix A satisfying the condition |an,2k−1| + |an,2k| ≤ M|ank| on the matrix A = (ank) for each n,k = 1,2,··· and each p,0 < p ≤ ∞ the set of A−p type operators is a linear space and raised an open question whether this condition is necessary to be a linear space? In this paper we have answered the question in negation. Further, we have introduced and studied the class A (s) −p of s-type cesp operators using s-number sequence and Cesaro sequence spaces. We have also shown that the class A (s) − p forms a quasi-Banach operator ideal. Moreover, the inclusion

Approaches to Conditional Risk

We present and compare two different approaches to conditional risk measures. One approach draws from convex analysis in vector spaces and presents risk measures as functions on Lp spaces, while the other approach utilizes module-based convex analysis where conditional risk measures are defined on Lp type modules. Both approaches utilize general duality theory for vector valued convex functions in contrast to the current literature in which we find ad hoc dual representations. By presenting several applications such as monotone and (sub)cash invariant hulls with corresponding examples we illustrate that module-based convex analysis is well suited to the concept of conditional risk measures.