Bilinearity rank of the cone of positive polynomials and related cones

For a proper cone K ⊂ Rn and its dual cone K the complementary slackness condition xT s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K^* }. When K is a symmetric cone, this manifold can be described by a set of n bilinear equalities. When K is a symmetric cone, this fact translates to a set of n linearly independent bilinear identities (optimality conditions) satisfied by every (x, s) ∈ C(K). This proves to be very useful when optimizing over such cones, therefore it is natural to look for similar optimality conditions for non-symmetric cones. In this paper we define the bilinearity rank of a cone, which is the number of linearly independent bilinear identities valid for the cone, and describe a linear algebraic technique to bound this quantity. We examine several well-known cones, in particular the cone of positive polynomials P2n+1 and its dual, the closure of the moment cone M2n+1, and compute their bilinearity ranks. We show that there are exactly four linearly independent bilinear identities which hold for all (x,s) ∈ C(P2n+1), regardless of the dimension of the cones. For nonnegative polynomials over an interval or half-line there are only two linearly independent bilinear identities. These results are extended to trigonometric and exponential polynomials

Bilinearity rank of the cone of positive polynomials and related cones

For a proper cone K ⊂ Rn and its dual cone K the complementary slackness condition xT s = 0 defines an n-dimensional manifold C(K) in the space { (x, s) | x ∈ K, s ∈ K^* }. When K is a symmetric cone, this manifold can be described by a set of n bilinear equalities. When K is a symmetric cone, this fact translates to a set of n linearly independent bilinear identities (optimality conditions) satisfied by every (x, s) ∈ C(K). This proves to be very useful when optimizing over such cones, therefore it is natural to look for similar optimality conditions for non-symmetric cones. In this paper we define the bilinearity rank of a cone, which is the number of linearly independent bilinear identities valid for the cone, and describe a linear algebraic technique to bound this quantity. We examine several well-known cones, in particular the cone of positive polynomials P2n+1 and its dual, the closure of the moment cone M2n+1, and compute their bilinearity ranks. We show that there are exactly four linearly independent bilinear identities which hold for all (x,s) ∈ C(P2n+1), regardless of the dimension of the cones. For nonnegative polynomials over an interval or half-line there are only two linearly independent bilinear identities. These results are extended to trigonometric and exponential polynomials

Concerns of Women of Reproductive Age with Multiple Sclerosis: A Qualitative Study

AbstractIntroduction: Psychological disorders are the leading cause of disabilities, socialharms, and reduced quality of life in patients with Multiple Sclerosis (MS). Thisqualitative study was conducted to describe the concerns of females with MS.Methods: In this qualitative study, 16 females with MS at the reproductive agewith medical records at the MS Society of Tabriz were selected using the purposivesampling technique and underwent semi-structured in-depth individual interviews.All interviews were recorded, transcribed, and analyzed using conventional contentanalysis.Results: In this study, 23 codes were identified from transcribed interviews andcategorized to two sub-categories, fears and feelings. These two sub-categories formedthe main category, named concerns.Conclusions: Regarding concerns of these patients, their regular health monitoring byphysicians and healthcare providers is recommended in an attempt to alleviate theseconcerns

Developments in the Principle of the Right to Receive Medical Assistance in the Event of Disasters in the Light of International soft Law

تعداد معدودی از اسناد الزام­آور بین­المللی به مسئله حق بر دریافت امدادهای پزشکی در واکنش به بلایای طبیعی و انسانی وجود دارد. اما در سال­های اخیر اسناد حقوق نرم در این زمینه توسعه پیدا کرده­اند که از جمله آن­ها می­توانیم به پیش­نویس مواد مربوط به حفاظت از افراد در هنگام وقوع بلایا مصوب کمیسیون حقوق بین­ الملل، اصول راهنمای ملل متحد در مورد جا به جایی داخلی، کد رفتاری صلیب سرخ و هلال احمر و منشور بشردوستانه و حداقل استانداردها در واکنش به بلایا اشاره کنیم. علی­رغم این­که این اسناد دارای ویژگی الزام­آوری نیستند، اما می­توانند در ایجاد همگرایی و هماهنگی میان بازیگران بین­المللی جهت ارائه امدادهای پزشکی نقش مهمی را ایفا کنند. به بیان ساده­تر، این اسناد غیرالزام­آور در فرآیند شکل­گیری عرف­های بین­المللی به نقش­آفرینی می­پردازند. از طرفی، کمیسیون حقوق بین­الملل در پیش­نویس مواد مربوط به حفاظت از افراد در هنگام وقوع بلایا این نکته مهم را مدنظر قرار داده است که استانداردها و هنجارهای غیرالزام­آور برای توسعه چهارچوب حقوقی قابل قبول بین­المللی برای حفاظت از قربانیان بلایا ضروری است. با توجه به این اهمیت، در پژوهش حاضر برای درک بهتر اصول و استانداردهای مربوط به کمک­های بشردوستانه باید به بررسی مفاد این اسناد بپردازیم.There is a small number of binding international documents on the issue of the right to receive medical assistance in response to natural and man-made disasters. In recent years, however, soft law instruments have been developed in this area, including the draft articles on the protection of persons in the event of a disaster, adopted by the UNHCR, the UN Guidelines on Internal Displacement, and the Code of Conduct for the Red Cross. And mention the Red Crescent and the humanitarian charter and the minimum standards in response to disasters. Although these documents are not binding, they can play an important role in creating convergence and coordination among international actors to provide medical assistance. Simply put, these non-binding documents play a role in the process of shaping international customs. On the other hand, in drafting articles on the protection of persons in the event of a disaster, the International Law Commission has taken into account the importance of non-binding standards and norms to develop an internationally acceptable legal framework for the protection of victims of disasters. Given this importance, in the present study, in order to better understand the principles and standards related to humanitarian aid, we should examine the provisions of these documents.   Please cite this article as: Alizadeh Y, Masoudinia M, Rostami S, Beyranvand F. Developments in the Principle of the Right to Receive Medical Assistance in the Event of Disasters in the Light of International Soft Law. Med Hist J 2016; 8(28): 85-103

Study of Nitrate Transfer in Corn Fodder Cultivation using Treated Urban Wastewater as Reuse water (Case Study: Neyshabur Sewage Treatment Plant Effluent)

Agricultural irrigation with treated wastewater effluent may be used for crop production, but due to elevated of certain contaminants (e.g. nitrate or nitrite) may adversely impact the quality of groundwater. This research was carried out to investigate the transfer of nitrate in deep soil that was planted with corn fodder crop using treated effluent from the sewage treatment plant in the city of Neyshabur during 2012-2013. The study data were collected in pot cultivation with the same condition and under a completely randomized design. The irrigation with wastewater effluent and conventional raw water was performed at four levels comprised of: 100% irrigation capacity and 80% irrigation capacity for two irrigation periods of 8 and 10 days and 3 replications. The result of this study showed that irrigation levels and irrigation periods affected the absorption of nitrate by corn. Comparison of the amount of nitrogen in wastewater effluent and conventional raw water before and after irrigation showed that the nitrate absorption in the plant was low (below the standard level) and there is no significant health issue for the users of the corn forage components in the food chain. Also, the average nitrate concentration (on mass basis) of wastewater effluent after irrigation (drainage water) was about 64 mg/kg and the nitrate content in the soil under irrigation was about 59 mg/kg. Irrigation of corn with treated wastewater does not increase the health hazards of the crop and the soil, but there is still a high risk of nitrate pollution for the water resources in the area

Circulating and Endometrial Profiles of miR-145, miR-155-5p, miR-224, MPP-5, and PECAM-1 Expression in Patients with Repeated Implantation Failure: A Case Control Study

Objective: An association between microRNAs (miRNAs) and adhesion proteins expression with repeated implantationfailure (RIF) has been recently reported; however, these findings are controversial. This study aims to evaluatethe endometrial and circulating expressions of miR-145, miR-155-5p, and miR-224 in addition to the endometrialexpressions of membrane protein palmitoylated-5 (MPP-5) and endothelial cell adhesion molecule-1 (PECAM-1) inpatients with RIF compared to control subjects.Materials and Methods: This case-control study was carried out between June 2021-July 2022. Subjects included 17patients with RIF and 17 control subjects, who had previous spontaneous term pregnancy with a live birth, who referredto the Medical Centre of Arash Hospital, Tehran, Iran. Endometrial tissue samples were obtained via hysteroscopyand Pipelle catheter in the RIF and control subjects, respectively. Plasma samples were collected after ovulationin all subjects. The expression levels of MPP5, PECAM-1, miR-224, miR-145, and miR-155-5p were evaluated byquantitative real-time polymerase chain reaction (qRT-PCR). The student’s t test, chi-square, Mann-Whitney U, andanalysis of covariance (ANCOVA) were used for data analyses.Results: RIF patients had less endometrial miR-155-5p expression, and higher endometrial and circulating expressions ofmiR-145 and miR-224 compared to control subjects. Endometrial PECAM-1 and MPP5 expression significantly decreased inpatients with RIF compared to the control group. There was a positive correlation between circulating miR-224 and endometrialmiR-155-5p, and between circulating miR-155-5p and endometrial PECAM-1 expression levels in patients with RIF.Conclusion: The present study suggests that circulating miR-224, endometrial miR-145, and PECAM-1 can bereliable, novel biomarkers for diagnosis of RIF