INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK

In this paper, we consider a class of meromorphic functions $r(z)$ having an $s$-fold zero at the origin and establish some inequalities of Bernstein and Turán type for the modulus of the derivative of rational functions  in the sup-norm on the disk in the complex plane. These results produce some sharper inequalities while taking into account the placement of zeros of the underlying rational function. Moreover, many inequalities for polynomials and polar derivatives follow as special cases. In particular, our results generalize as well as refine a result due Dewan et al. [6].

My Memoirs

H. R. H. Sardar Shah Wali, the surviving uncle of His Majesty King Mohammed Zahir Shah of Afghanistan, was born in Debra Dun (India) in 1888. He studied Persian (Dari), Pashto, English and Urdu privately under the guidance of competent tutors. In 1901, the Sardar returned to his motherland with all the members of his family, and was warmly received at Kabul by Amir Abdur Rahman, ruler of Afghanistan. Sardar Shah Wali continued his studies until 1906 with emphasis on military science, and subsequently played a most important part in public affairs and in shaping the destinies of his homeland. Since his political and military knowledge fitted him for a military post, he was appointed the Officer of the Royal Bodyguard. In addition to this important post, he worked as Aid-de-Camp to His Majesty Amir Habibullah Khan.https://digitalcommons.unomaha.edu/ascdigitizedbooks/1017/thumbnail.jp

Splainidega lahendamine

Dissertatsioonis on käsitletud kolme probleemi splainide teooriast. Esiteks vaadeldakse kuupsplainidega histopoleerimist. Antud on suvaliselt paiknevate sõlmedega ja suvaliste kõrgustega histogramm. Näidatakse, et alati on olemas histopoleeriv kuupsplain üldka-su¬tatavate rajatingimuste korral. Splaini leidmisel kasutatakse erinevaid esitusi. Teiseks uuritakse suvalise võrgu korral histopoleeriva polünomiaalse perioodilise splaini ole¬mas-olu. Saadud tulemustest järelduvad kirjandusest varem teadaolevad tulemused ühtla¬se võrgu korral. Kolmas probleem, mida dissertatsioonis lahendatakse, on ruut/lineaar ratsionaalsplainidega histopoleerimine. Taolised splainid säilitavad lähteandmete kume-ru¬se, sest nad on ise alati selle omadusega. Et vabadus on siin splaini sõlmede valikus, on loomulik küsida, kas suvalise rangelt kumera histogrammi korral on võimalik valida splaini sõlmed nii, et eksisteeriks histopoleeriv ruut/lineaar ratsionaalsplain. Vastus on siin eitav. Uurimisel leitakse splaini parameetreid määrav baasvõrrandite süsteem ning splaini eksisteerimine on samaväärne selle mittelineaarse süsteemi lahendi olemasoluga. Probleemi lahendamiseks on leitud splaini sobiv esitus.The dissertation treats three kinds of problems from the theory of splines. Firstly, a par¬ti-cular interpolation problem about the cubic spline histopolation with arbitrary place¬ment of histogram knots and spline knots between them is discussed. A cubic spline is studied provided that its integral on a prescribed interval equals the area of the corres¬pon¬ding histogram rectangle. It is considered the most common boundary value con¬di¬tions like given values of the spline and its first and second derivatives in endpoints of given interval and then solved the problem of existence and uniqueness of the solution for such histopolation problem. Secondly, the periodic polynomial spline histopolation problem with the arbitrary placement of histogram knots and coinciding histogram knots is considered. Several results about the existence and uniqueness of solution are obtained and they imply known results in the case of uniform grid. In the last problem, the rational spline histopolation of convex data is studied. For the concern about the con¬vexity, an appropriate tool is interpolation or histopolation with quadratic/linear rational splines because these splines keep the sign of its second derivative on the whole interval. For this reason the given histogram is assumed to be strictly convex. The main task is at the study of existence of solution for a nonlinear system of basic equations to determine the values of second derivatives in spline knots. The other parameters in the representation of spline are determined from a linear system with regular matrix. It is shown that there is a strictly convex histogram without the solution of histopolation problem for any choice of spline knots.https://www.ester.ee/record=b524283

ON CAUCHY-TYPE BOUNDS FOR THE EIGENVALUES OF A SPECIAL CLASS OF MATRIX POLYNOMIALS

Let $\mathbb{C}^{m\times m}$ be the set of all $m\times m$ matrices whose  entries are in $\mathbb{C},$ the set of complex numbers. Then $P(z):=\sum\limits_{j=0}^nA_jz^j,$ $A_j\in \mathbb{C}^{m\times m},$ $0\leq j\leq n$ is called a matrix polynomial. If $A_{n}\neq 0$, then $P(z)$ is said to be a matrix polynomial of degree $n$. In this paper we prove some results for the  bound estimates of the eigenvalues of some lacunary type of matrix polynomials

The Effect of Training and Development Practices on Employees’ Organizational Commitment among the Employees in Private Health Care Sector in Khyber Pakhtunkhwa, Pakistan

This study examined the relationship between training and development practices, and organizational commitment for a sample of employees working in private healthcare sector in Khyber Pakhtunkhwa, Pakistan. The results showed that training and development practices were positively related to organizational commitment. To examine this relationship, a survey was conducted on 134 employees working in private healthcare sector in Khyber Pakhtunkhwa, Pakistan, selected randomly. Correlation and regression analysis techniques were used to analyze the relationship of training and development practices and organizational commitment. The results of the study showed that organizational commitment of private healthcare sector employees were dependent on the training and development practices

Tubercular tenosynovitis of extensor tendons of foot--a rare presentation of musculoskeletal tuberculosis in an infant

Tuberculosis of soft tissues as a result of spread from adjacent bone or joint is a well recognized entity. However isolated tuberculous pyomyositis, bursitis and tenosynovitis are rare, constituting about 1% of skeletal tuberculosis. Tubercular tenosynovitis commonly involves tendon sheaths of wrist and hand. Cases of tuberculous tenosynovitis of foot and ankle are rare. A rare case of tubercular tenosynovitis of extensor tendons in a one year child has been reported here with its clinical presentation, treatment and a brief review of literature.Keywords: Tuberculosis; Musculoskeletal; TenosynovitisInternet Journal of Medical Update 2012 July;7(2):45-4

Results of Lumbar Transpedicular Fixation for Spondycolisthesis, in Terms of Back Pain Relief

Objective:  The goal of this study was to see how transpedicular fixation for degenerative spondylolisthesis affected lumbago. Methodology:  A retrospective observational study was conducted at the Department of Neurosurgery in Hayatabad Medical Complex, Peshawar between May 2018 and February 2020. Degenerative spondylolisthesis was diagnosed using static and dynamic spinal X-rays. The research excluded the patients with grade 5 spondylolisthesis, congenital anomalies, or prior spinal surgery. The visual rating scale was used to assess pain alleviation (GRS). Dynamic or static lumbosacral X-rays and 3D CT scans were used to assess union. Results:  In total 70 patients, 38 (54.3%) were male and 32 (45.7%) were female. L5–S1 was impacted in most of the cases (68%). 40% of patients were having Meyerding grade II. All patients had pedicle screw fixation. Following surgery, 44 (63%) patients reported no pain, and 12 (17%) patients reported mild discomfort. 8 (11%) patients reported moderate pain and 6(9%) patients experienced severe pain. There existed a significant difference between pre/postoperative moderate-severe GRS scores (p-value: 0.000336). After surgery, we were able to negotiate surgical unions with 91.4% of the patients. Conclusion:  For individuals with spondylolisthesis who need pain relief, transpedicular fixation is a safe, straightforward, and effective treatment. It also aids with the surgical union and the improvement of the neurological condition. Keywords:  Spondylolisthesis, Meyerding grading, Transpedicular fixation

LEARNING ORIENTATION AND PERFORMANCE: THE INTERACTION EFFECT OF ENTREPRENEURIAL ORIENTATION

The current study examines the impact of learningorientation (LO) on organizational performance and also themoderating role of entrepreneurial orientation (EO) on therelationship between LO and organizational performance amongthe small and medium enterprises (SMEs) in Pakistan. Thisquestionnaire survey was conducted among 213 managers/ ownersof manufacturing SMEs. Previous studies on LO in combinationwith EO have been conducted in large organizations in developedeconomies. Studying the relationship between LO and performanceand moderated by EO in manufacturing SMEs in a developingeconomy like Pakistan, this research attempts to fill this gap. Thefindings reveal that there exist a positive relationship between LOand organizational performance. The findings also demonstratethat the effects of LO on organizational performance are positivelymoderated by EO. The paper also includes research implicationsand possible future directions

Job behaviors and their impact on Performance Appraisal Effectiveness: Conceptual Propositions

The current study is a prepositional study which looks employee behaviours and their impact on human resource intervention effectiveness. It is a literature based study. Extant literature has been explored and relationships have been presented in a new way. The study is the first one in conceptually presenting new insights. The study is believed to open a fresh research discussion. It has theoretical implications. The study recommends empirical testing of the proposition presented in this study. The study has all the limitations of a social science research