On the Cauchy problem of dispersive Burgers type equations

We study the paralinearised weakly dispersive Burgers type equation: $$\partial_t u+\partial_x [T_u u]-T_{\frac{\partial_x u}{2}}u+\partial_x |D|^{\alpha-1}u=0,\ \alpha \in ]1,2[,$$ which contains the main non linear "worst interaction" terms, i.e low-high interaction terms, of the usual weakly dispersive Burgers type equation: $$\partial_t u+u\partial_x u+\partial_x |D|^{\alpha-1}u=0,\ \alpha \in ]1,2[,$$ with $u_0 \in H^s(\mathbb D)$, where $\mathbb D=\mathbb T \text{ or } \mathbb R$. Through a paradifferential complex Cole-Hopf type gauge transform we introduce for the study of the flow map regularity of Gravity-Capillary equation, we prove a new a priori estimate in $H^s(\mathbb D)$ under the control of $\left\Vert(1+\left\Vert u\right\Vert_{L^\infty_x})\left\Vert u \right\Vert_{W^{2-\alpha,\infty}_x}\right\Vert_{L^1_t}$, improving upon the usual hyperbolic control $\left\Vert \partial_x u\right\Vert_{L^1_tL^\infty_x}$. Thus we eliminate the "standard" wave breaking scenario in case of blow up as conjectured by J. C. Saut and C. Klein in their numerical study of the dispersive Burgers equation. For $\alpha\in ]2,3[$ we show that we can completely conjugate the paralinearised dispersive Burgers equation to a semi-linear equation of the form: $$\partial_tu+ \partial_x |D|^{\alpha-1}u=R_\infty(u),\ \alpha \in ]2,3[,$$ where $R_\infty$ is a regularizing operator under the control of $\left\Vert u\right\Vert_{L^\infty_t C^{2-\alpha}_*}$

Regularity results on the flow maps of periodic dispersive Burgers type equations and the Gravity-Capillary equations

In the first part of this paper we prove that the flow associated to a dispersive Burgers equation with a non local term of the form $|D|^{\alpha-1} \partial_x u$, $\alpha \in [1,+\infty[$ is Lipschitz from bounded sets of $H^s_0(\mathbb T;\mathbb R)$ to $C^0([0,T],H^{s-(2-\alpha)^+}_0(\mathbb T;\mathbb R))$ for $T>0$ and $s>1+\frac{2-\alpha}{\alpha-1}+\frac{1}{2}$, where $H^s_0$ are the Sobolev spaces of functions with $0$ mean value. The proof relies on a paradifferential generalization of a complex Cole-Hopf gauge transformation introduced by T.Tao for the Benjamin-Ono equation. For this we prove a generalization of the Baker-Campbell-Hausdorff formula for flows of hyperbolic paradifferential equations and prove the stability of the class of paradifferential operators modulo more regular remainders, under conjugation by such flows. For this we prove a new characterization of paradifferential operators in the spirit of Beals. In the second part of this paper we use a paralinearization version of the previous method to prove that a re-normalization of the flow of the one dimensional periodic gravity capillary equation is Lipschitz from bounded sets of $H^s$ to $C^0([0,T],H^{s-\frac{1}{2}})$ for $T>0$ and $s>3+\frac{1}{2}$

A geometric proof of the Quasi-linearity of the water-waves system

In the first part of this paper we prove that the flow associated to the Burgers equation with a non local term of the form $H\langle D \rangle^\alpha u$ fails to be uniformly continuous from bounded sets of $H^s({\mathbb D})$ to $C^0([0,T],H^s({\mathbb D}))$ for $T>0$, $s>\frac{1}{2}+2$, $0\leq \alpha <2$, ${\mathbb D}={\mathbb R} \ \text{or} \ {\mathbb T}$ and $H$ is the Hilbert transform. Furthermore we show that the flow cannot be $C^1$ from bounded sets of $H^s({\mathbb D})$ to $C^0([0,T],H^{s-1+(\alpha-1)^+ +\epsilon}({\mathbb D}))$ for $\epsilon>0$. We generalize this result to a large class of nonlinear transport-dispersive equations in any dimension, that in particular contains the Whitham equation and the paralinearization of the water waves system with and without surface tension. The current result is optimal in the sense that for $\alpha=2$ and ${\mathbb D}={\mathbb T}$ the flow associated to the Benjamin-Ono equation is Lipschitz on function with $0$ mean value $H^s_0$. In the second part of this paper we apply this method to deduce the quasi-linearity of the water waves system, which is the main result of this paper

The Impact of Applying Quality Standards on the Internal Operations in the Public Sector in the Sultanate of Oman

Purpose:  The aim of this study is to identify the impact of applying quality standards on the internal operations efficiency in public sector institutions in the Sultanate of Oman along with measuring the effectiveness and efficiency of operations after applying quality standards.   Theoretical framework: This study focuses on the definition of quality and its history, quality standards, its types, rational behind their application, continuous improvement methodology which is Deming cycle (plan, Do, check, Act), and defining internal processes and their dimensions.   Design/Methodology/Approach: To achieve the objective of this study , the questionnaire was used as a main tool for data collection. Questionnaires were distributed to a simple random sample of 115; 107, questionnaires were retrieved and (102) were suitable for analysis. The data was then analyzed using a variety of statistical techniques (arithmetic means and standard deviations, multiple linear regression analysis using the stepwise method, and Cronbach alpha for stability).   Findings: The main findings in this study was identifies that prove there is a gap between quality standereds applications in planning of operations, readiness, and outputs.   Research /Practical /Social Implications: This study is significant since it focuses on the influence of applying quality standards in terms of results and effect, specifically on processes and whether there is continuous process improvement. In social indicator it is impacting individuals satisfactions specially when speaking about the customers experience. Moreover, in enconmoical indocators it is indicates improvement of the institutional performance.   Originality/ Value: This study is distinguished from previous studies in that it focuses on the impact of applying quality standards in terms of results and effect, specifically on processes. Moreover, this study specially build based on Oman experience.

On the Gamma-Logistic Distribution

A new generalization of the logistic distribution is defined and studied, namely, the gamma-logistic distribution. Various properties of the gamma-logistic are obtained. The structural analysis of the distribution includes moments, mode, quantiles, skewness, kurtosis, Shannon\u27s entropy and order statistics. The method of maximum likelihood estimation is proposed for estimating the model parameters. For illustrative purposes, a real data set is analyzed as an application of the gamma-logistic distribution

Awareness, attitude and preference of long-acting reversible contraceptives by Tanta University contraceptive clinic attendants

Background: Long Acting Reversible Contraceptives (LARC) had a very high efficacy in lowering unintended pregnancies and their poor health sequalae. Although their reported efficacy, these methods are not widely used among patient’s due to non-awareness and faulty concepts linked to these methods.Methods: This cross-sectional study was conducted to determine the degree of awareness, attitude and preference of LARC by attendants of Tanta University contraceptive clinic in the period from January 1, 2016 to December 31, 2016. All patients were counseled with thorough discussion about LARC methods. The following issues were determined: age, parity, mode of previous delivery, residence, medical diseases, socioeconomic state of family, type of LARC method used, how she know about this method and why she preferred that type.Results: 391 women underwent this study with age range of 21-46 years, and BMI range of 20.46-31.87. LARC were preferred by 72.38% of patients and mainly IUDS (52.94%) while other LARC methods were of very low awareness. Most patients take their knowledge from paramedical staffs (49.87%). Occupation, education, residence and religion were not affecting patients' attitude and preference of one LARC over the other methods. Age was the most effective factor for determining whether to use LARC or not. Counseling revert a lot of faulty concepts and misbelieves about LARC.Conclusions: LARC were not widespread among Tanta University attendants for contraception except for IUDs. Young patients had no motivations towards LARC due to a lot of faulty concepts that need a lot of work to be eradicated

Acupressure for Chemotherapy Induced Nausea and Vomiting in Breast-Cancer Patients: A Randomized, Placebo-Controlled Clinical Trial

Introduction: Chemotherapy is an important treatment in cancer (CA) care and is associated with numerous side effects. Early studies reported that patients cited nausea and vomiting as the most distressing symptoms when receiving chemotherapy. Despite continuing improvements in antiemetic therapies, nausea and vomiting following chemotherapy treatment for CA remains a significant clinical problem for many patients and there is correlation between the intensity of anticipatory nausea in the clinic prior to their treatment infusion and subsequent post treatment of nausea and vomiting. Since pharmacological treatments have failed to completely manage nausea and vomiting, exploring the complementary, non-pharmacological, approaches that can be used in addition to pharmacological approaches becomes paramount. Acupressure at the P6 point is a value-added technique in addition to pharmaceutics; management for women undergoing treatment for breast cancer to reduce the incidence and intensity of delayed chemotherapy induced nausea and vomiting (CINV), since up to 60% of patients had been reported nausea despite the use of antiemetics Aims: The first aim  is to examine the efficacy of P6-acupressure in preventing chemotherapy induced nausea and emesis associated with highly emetogenic chemotherapy (i.e. doxorubicin as adjuncts to standard 5-HT3 antiemetics (granisetron) and dexamethasone antiemetic given as part of routine care in reducing acute nausea (during the day of treatment) and delayed nausea (2-5 days) following the day of chemotherapy. The second aim is to examine the efficacy of the acupressure bands in reducing vomiting and in maintaining Quality of Life (QOL). Patients and methods: A randomised, double-blind, placebo controlled trial. One group received acupressure with bilateral stimulation of P6 (n=42), a second group received bilateral placebo stimulation, (n=42) and a third group received no acupressure wrist band and served as a control group, (n=42). Acupressure was applied using a Sea-Band (Sea- Band UK Ltd., Leicestershire, England) which had to wear for the 5 days following the chemotherapy administration. Assessments of acute and delayed nausea and emesis, OOL, patients' satisfaction, recommendation of treatment and requirement of rescue antiemetic were obtained. Results: No significant differences were found in the incidence of acute nausea or emesis 24- h following chemotherapy by treatment groups. Significant difference was found in the severity of early nausea (0-6 scale) in the acupressure group M (SD) 1.62 (2.04) as compared to placebo group 2.17 (2.09), p=, 0006. The acupressure group had a statistically significant reduction in the incidence of delayed nausea 40% (17/42) as compared to the control group 62% (26/42) (p= ,0495). Further analyses indicated that significant difference existed in the intensity of delayed nausea by acupressure group mean (SD) 1.45 (1.73), p=, 0002 as compared to control 2.03 (1.91). Significant difference also existed in the intensity of delayed nausea by placebo group 1.33 (1.66), p=, 0010 as compared to control 2.03 (1.91). Here we noted a placebo effect. The percentage of the patients who had delayed moderate to very severe nausea day 2-5 (≥3 on 0-6 scale) in the acupressure group is 55% (23/42 (p= 0206), in the placebo group 52% (22/42) (p= 0116), a statistically significant reduction existed as compared to control 79% (33/42). Here we noted a placebo effect. The incidence of delayed vomiting episodes day 2-5 was 48% (20/42), 64% (27/42), and 57% (24/42) in the acupressure, placebo and control group respectively. No significant differences were found between the groups. The mean of number of delayed emetic episodes day 2-5 was significantly less in the acupressure group 2.7 (1.87) as compared to placebo 3.3 (1.91), p=,0022 and control groups 2.07(1.20), P= ,0005. Requirement of rescue antiemetic was significantly lower in P6-acupressure (55%, 23/42), as compared to control group (76%, 32/42) (p= 0389). 81% (35/42)) of the patients in acupressure group were significantly satisfied with P6-acupressure as compared to placebo group 64% (27/42), p= 0.0471. 79% (34/42)) of the patients in acupressure group would recommend P6-acupressure to another patients as compared to placebo group 62% (26/42), p= 0,0533 . No statistically significant differences between groups were observed for the overall items response rate of the FACT-Scale which were 74/108, 67/108, 69/108 in the acupressure, placebo and control group respectively. Conclusion: P-6 Acupressure is efficacious for control of delayed chemotherapy related nausea and emesis and is a value-added method in addition to pharmaceutical management for women undergoing treatment for breast cancer. Placebo effect of acupressure decreased severity of delayed nausea day 2-5 but the mean of number of delayed emetic episodes and need of rescue antiemetics were reduced only by acupressure with the correct P6 point stimulation. Keywords: breast cancer, chemotherapy, nausea, vomiting, acupressure.

On paracomposition and change of variables in Paradifferential operators

In this paper we revisit the hypothesis needed to define the "paracomposition" operator, an analogue to the classic pull-back operation in the low regularity setting, first introduced by S. Alinhac. More precisely we do so in two directions. First we drop the diffeomorphism hypothesis. Secondly we give estimates in global Sobolev and Zygmund spaces. Thus we fully generalize Bony's classic paralinearasition Theorem giving sharp estimates for composition in Sobolev and Zygmund spaces. In order to prove that the new class of operations benefits of symbolic calculus properties when composed by a paradifferential operator, we discuss the pull-back of pseudodifferential and paradifferential operators which then become Fourier Integral Operators. In this discussion we show that those Fourier Integral Operators obtained by pull-back are pseudodifferential or paradifferential operators if and only if they are pulled-back by a diffeomorphism i.e a change of variable. We give a proof of the change of variables in paradifferential operators. Finally we give a cutoff defining paradifferential operators that is stable by successive composition. This permits the definition and convergence in the class of paradifferential operators of series, for example the exponential of a paradifferential operator of negative order. This is the main new technical result of this paper.Comment: In the new version we added the refined study of the cut-off after composition of two paradifferential operator