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Open Journal of Mathematical Science (OMS)

ISSN: 2523-0212 (online) 2616-4906 (Print)

Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (online) 2616-8103 (Print)

Open Journal of Discrete Applied Mathematics (ODAM)

ISSN: 2617-9687 (online) 2617-9679 (Print)

Ptolemy Journal of Chemistry (PJC)

ISSN: 2618-0758 (online) 2618-074X (Print)

Engineering and Applied Science Letters (EASL)

ISSN: 2617-9709 (online) 2617-9695 (Print)

Trends in Clinical and Medical Sciences (TCMS)

ISSN: 2791-0814 (online) 2791-0806 (Print)

Our Journals

Open Journal of Mathematical Science (OMS)

ISSN: 2523-0212 (online) 2616-4906 (Print)

Open Journal of Mathematical Analysis (OMA)

ISSN: 2616-8111 (online) 2616-8103 (Print)

Open Journal of Discrete Applied Mathematics (ODAM)

ISSN: 2617-9687 (online) 2617-9679 (Print)

Ptolemy Journal of Chemistry (PJC)

ISSN: 2618-0758 (online) 2618-074X (Print)

Engineering and Applied Science Letters (EASL)

ISSN: 2617-9709 (online) 2617-9695 (Print)

Trends in Clinical and Medical Sciences (TCMS)

ISSN: 2791-0814 (online) 2791-0806 (Print)

Latest in Press

Author(s): Mamman Ojima John1, Aboiyar Terhemen1, Tivde Tertsegha1
1Department of Mathematics/Statistics/Computer Science, Faculty of Science, Federal University of Agriculture Makurdi, Benue State, Nigeria.
Abstract:

This research presents the solution of the generalized version of Abel’s integral equation, which was computed considering the first and second kinds. First, Abel’s integral equation and its generalization were described using fractional calculus, and the properties of Orthogonal polynomials were also described. We then developed a technique of solution for the generalized Abel’s integral equation using infinite series of orthogonal polynomials and utilized the numerical method to approximate the generalized Abel’s integral equation of the first and second kind, respectively. The Riemann-Liouville fractional operator was used in these examples. Our technique was implemented in MAPLE 17 through some illustrative examples. Absolute errors were estimated. In addition, the occurred errors between using orthogonal polynomials for solving Abel’s integral equations of order \(0\ <\ \alpha \ <\ 1\) and the exact solutions show that the orthogonal polynomials used were highly effective, reliable and can be used independently in situations where the exact solution is unknown which the numerical experiments confirmed.

Author(s): Badibi O. Christopher1, Ramadhani I.2, Ndondo M. Apollinaire1, Kumwimba S. Didier1
1Département de Mathématiques et Informatique (RDC), Faculté des Sciences, Université de Lubumbashi, Democratic Republic of the Congo.
2Département de Mathématiques, Informatique et Statistiques(RDC), Faculté des Sciences et Technologies, Université de Kinshasa, Democratic Republic of the Congo.
Abstract:

Stochastic differential equations (SDEs) are a powerful tool for modeling certain random trajectories of diffusion phenomena in the physical, ecological, economic, and management sciences. However, except in some cases, it is generally impossible to find an explicit solution to these equations. In this case, the numerical approach is the only favorable possibility to find an approximative solution. In this paper, we present the mean and mean-square stability of the Non-standard Euler-Maruyama numerical scheme using the Vasicek and geometric Brownian motion models.

Author(s): Bitrus Sambo1, Timothy Oloyede Opoola2
1Department of Mathematics, Gombe State University, P.M.B. 127, Gombe, Nigeria.
2Department of Mathematics, University of Ilorin, P.M.B. 1515, Ilorin, Nigeria.
Abstract:

Using opoola differential operator, we defined a subclass \(S^{n}_{p}(\lambda,\alpha,\gamma,\delta)\) of the class of multivalent or p-valent functions. Several properties of the class were studied, such as coefficient inequalities, hadamard product, radii of close-to-convex, star-likeness, convexity, extreme points, the integral mean inequalities for the fractional derivatives, and further growth and distortion theorem are given using fractional calculus techniques.

Author(s): J. B. Omosowon1, A. Y. Akinyele1, F. Y. Aderibigbe1
1Department of Mathematics, University of Ilorin, Ilorin, Nigeria.
Abstract:

In this paper, we present results of \(\omega\)-order preserving partial contraction mapping generating a nonlinear Schr\”odinger equation. We used the theory of semigroup to generate a nonlinear Schr\(\ddot{o}\)dinger equation by considering a simple application of Lipschitz perturbation of linear evolution equations. We considered the space \(L^2(\mathbb{R}^2)\) and of linear operator \(A_0$ by $D(A_0)=H^2(\mathbb{R}^2)\) and \(A_0u=-i\Delta u\) for \(u\in D(A_0)\) for the initial value problem, we hereby established that \(A_0\) is the infinitesimal generator of a \(C_0\)-semigroup of unitary operators \(T(t)\), \(-\infty<t<\infty\) on \(L^2(\mathbb{R}^2)\).

Author(s): Yüksel Soykan1, Erkan Taşdemir2, Inci Okumuş3
1Department of Mathematics, Art and Science Faculty, Zonguldak Bülent Ecevit University, 67100, Zonguldak, Turkey.
2Pınarhisar Vocational School, Kırklareli University, 39300, Kırklareli, Turkey
3Department of Engineering Sciences, Istanbul University-Cerrahpaşa, 34100, Istanbul, Turkey.
Abstract:

In this paper, closed forms of the sum formulas \(\sum\limits_{k=0}^{n}kx^{k}W_{k}\) and \(\sum\limits_{k=1}^{n}kx^{k}W_{-k}\) for generalized Tetranacci numbers are presented. As special cases, we give summation formulas of Tetranacci, Tetranacci-Lucas, and other fourth-order recurrence sequences.

Author(s): R. Pandiselvi1, M. Jeyaraman2, A. Ramachandran3
1PG and Research Department of Mathematics, The Madura College, Madurai-625011, Tamilnadu, India.
2PG and Research Department of Mathematics, Raja Doraisingam Government Arts College Sivagangai-630561, (Affiliated to Alagappa University, Karaikudi) Tamil Nadu, India.
3Suvarna Karnataka Institute of Studies and Research Center, Tumkur-572102, Karnataka, India.
Abstract:

This paper presents several fixed point theorems for intuitionistic generalized fuzzy metric spaces with an implicit relation. Specifically, we utilize compatible maps of type \((\beta)\) in intuitionistic generalized fuzzy metric spaces to derive our fixed point theorems. Our results not only extend but also generalize some fixed point theorems that were previously established in complete fuzzy metric spaces. This is achieved by introducing a novel technique, which enhances the applicability and scope of the existing fixed point theorems.

Author(s): Howard S. Cohl1, Roberto S. Costas-Santos2, Philbert R. Hwang3, Tanay V. Wakhare4
1Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
2Departamento de Métodos Cuantitativos, Universidad Loyola Andalucía, E-41704, Dos Hermanas, Seville, Spain.
3Card Technology Department, Capital One Financial Corporation, McLean, VA 22102, USA.
4Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Abstract:

We derive generalized generating functions for basic hypergeometric orthogonal polynomials by applying connection relations with one extra free parameter to them. In particular, we generalize generating functions for the continuous \(q\)-ultraspherical/Rogers, little \(q\)-Laguerre/Wall, and \(q\)-Laguerre polynomials. Depending on what type of orthogonality these polynomials satisfy, we derive corresponding definite integrals, infinite series, bilateral infinite series, and \(q\)-integrals.

Author(s): D. Ashok Kumar1, Ganesh Annamalai2, Nadar Kalaivani Venkatasami2, Sivabalan R G3
1Department of Anaesthesia and Pain, Tamilnadu Government Multi Super Speciality Hospital, Omandurar estate, Omandurar, Chennai, Tamil Nadu, India.
2Institute of Anaesthesiology & Critical Care Rajiv Gandhi Government general Hospital, Madras Medical College, Madras, India.
3Department of Anaesthesia, Institute of Anaesthesiology and Critical Care, Madras Medical College, Chennai, Tamil Nadu, India.
Abstract:

Background and Aim: Chronic cancer pain is one of the major challenges of palliative care and it is prevalent in 80\% of all the gastric and pancreatic malignancies. Adequate pain relief not only improves the drug compliance, but also alleviates depression among the cancer patients, thereby improving the quality of life. This study was carried out with the aim of evaluating the role of Coeliac Plexus ethanol Neurolysis (CPN) in pain relief among patients with gastric and pancreatic malignancy.
Methods and materials: This is an uncontrolled before-and-after non randomized trial. This bedside procedure was done in an ICU in chronic pain management centre. Trial coeliac plexus block was done after identification of coeliac trunk using ultrasound and 15 cc of 1% xylocard was given. After 30 minutes, pain relief was assessed with Numerical Rating Scale for pain (NRS). Patient was then given 20ml of 60% ethanol. Pain relief was documented using NRS immediately at 24hours, 72 hours,1 week and 3 months. Statistical analysis was done using Statistical Package for the Social Sciences version (SPSS) version 16.0. Paired t test was used to analyze the difference between variables.
Results: Our study shows statistically significant difference between pre-NRS and post immediate-NRS (mean 8.26\(\pm\)0.52 and 3.40 \(\pm\)0.47)(P value \(<0.0001\)) and significant decrease in NRS seen after 24 hours,72 hours,1 week and 3 months.
Conclusion: USG guided anterior approach coeliac plexus ethanol neurolysis is effective in decreasing pain associated with gastric and pancreatic malignancy.

Author(s): A. Umakanth1, Veera Purushotham1, Renuka Devi Nalluri1, Chennakesavulu Dara2, Phani Krishna Telluri2, Khizer 2
1Department Of General Medicine, ACSR Govt Medical College & Hospital Nellore, Andhra Pradesh-524004, India.
2Department Of General Medicine ESIC Medical College & Hospital Sanathanagar, Hyderabad-500038, India.
Abstract:

Background: With an estimated 13.3 million cases each year, acute kidney injury (AKI) become a problem for world health. India has a high prevalence of AKI following volume depletion from gastrointestinal fluid loss. Due to poor socioeconomic situations, limited access to care, lack of awareness of personal cleanliness, crowding, and climatic factors that encourage the spread of infection, diarrheal illnesses are widespread in India. AKI following gastroenteritis is probably caused by a lack of medical facilities in rural areas and a delay in treating dehydration. Therefore, in order to come up with solutions to this issue, it is necessary to comprehend the disease’s clinical spectrum.
Materials and Methods: This is a prospective observational study conducted on 50 patients with AKI due to Acute Gastroenteritis admitted to Narayana medical college \& hospital, Nellore, Andhra Pradesh, over a period of 1 year. The diagnosis of acute kidney injury was used when there was evidence of kidney injury in some clinical settings without any kidney disease history. The term acute kidney injury was used when there was a rise in Serum creatinine \(\geq44 \mu mol/L (\geq0.5mg/dL)\) and the history of decreased urine output of less than \(0.5ml/kg/hr\) for more than 6hrs. The criteria used for AKI in the study was Risk, Injury, Failure, Loss of kidney function, and End-stage kidney disease (RIFLE) criteria (given by Acute Dialysis Quality Initiative Group 2004) and is as follows.
Results: Pre Renal Azotemia, which occurred in 58% of cases, was followed by Acute Tubular Necrosis, which occurred in 42% of cases in this study. The pre-renal group’s mean age was \(49.3 + 5.66\) years, while the ATN group’s was \(48.6 + 7.40\) years. The mean age of those who survived was 46.73 4.75, while that of those who did not survive was 65 6.034. On admission, Baseline creatinine with a mean of \(3.032+0.37mg/dl\). It was \(2.70+0.29\) and \(3.48\pm0.77\) inpre-renal and Acute Tubular Necrosis (ATN) groups. The mean peak creatine was \(4.73+0.48mg/dl\). It was 4.13+ 0.59 in pre-renal and 5.56\(\pm\) 0.66 in ATN groups, respectively. The Mean creatinine at the time of discharge 2.87 \(\pm\) \(0.39mg/dl\). The mean peak creatinine was 2.42 \(\pm\) 0.33 in pre-renal & 3.48+0.42 in ATN groups (In survivors) and 4.11\(\pm\) 0.79 in non-survivors.
Conclusion: Replacement of lost fluids, correction of electrolyte imbalances, and delivery of the proper antibiotics made up the course of treatment. Due to the frequent incidence of hypokalemia, ARF brought on by gastroenteritis differs from other ARF and has a better prognosis. An significant electrolyte disruption in AKI brought on by gastroenteritis is hypokalaemia. It was determined that the primary factor leading to death in AKI caused by gastroenteritis is septicemia.

Author(s): Omar Al Awar1,2, Patricia Nehmeh2,3, Georgio Haddad2
1Neurosurgery Department, Mount Lebanon Hospital University Medical Center, Lebanon.
2University of Balamand, Lebanon.
3Department of Anesthesiology, Mount Lebanon Hospital University Medical Center, Lebanon.
Abstract:

Background: Awake brain surgery is used to treat brain tumors and epileptic seizures near areas that control language, movement or cognition, movement disorder, and recently during neurovascular surgery.
Methods: Preoperative airway evaluation should be performed in all patients. There are two commonly used anesthetic methods for awake craniotomy: monitored anesthesia care (MAC) and asleep-awake-asleep (AAA) technique, after the tumor resection, sedation is often sufficient until completion of the surgery. In our institution at Mount Lebanon hospital-Balamand university hospital, the combination of propofol and remifentanil has been considered as the standard protocol for sedation during the first stage of awake craniotomy because of the ease of use and reliability. The application of neuro-navigation, and intraoperative electrical mapping are a reliable method to minimize the risk of permanent deficit during surgery for brain tumors in eloquent areas.
Results: Whether sedation or an asleep-awake-asleep technique is chosen, it is crucial to apply adequate local anaesthesia on the skin incision what we call elliptic block using combinations of lidocaine and bupivacaine with epinephrine. If we perform awake-asleep-awake anesthesia type than similar to the pre-awake phase, one can also choose awake, spontaneous ventilation under light or deep sedation, or GA with airway control. Sedation often suffices. The patient usually requires lower rates of sedative infusions during the postawake phase than during the pre-awake phase as patients are often fatigued, and there is a lower level of painful stimuli during skull closure.
Conclusion: Patients receiving awake craniotomy have better outcomes in many aspects. The improvements in anesthetic agents and techniques, the application of neuro-navigation, and intraoperative electrical mapping are a reliable method to minimize the risk of permanent deficit during surgery. Appropriate patient selection, perioperative psychological support, and proper anesthetic management for individual patients in each stage of surgery are crucial for procedural safety, success, and patient satisfaction.

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