scholarly journals Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3320
Author(s):  
Daniela Marian ◽  
Sorina Anamaria Ciplea ◽  
Nicolaie Lungu
Keyword(s):  
Calculus Of Variations ◽  
Direct Method ◽  
Integral Form ◽  
Ulam Stability ◽  
Euler’S Equation ◽  
First Case ◽  
Special Cases ◽  
Euler's Equation ◽  
The Laplace Transform ◽  
First Time

In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus of variations in two special cases: when F=F(x,y′) and when F=F(y,y′). For the first case we use the direct method and for the second case we use the Laplace transform. In the first Theorem and in the first Example the corresponding estimations for Jyx−Jy0x are given. We mention that it is the first time that the problem of Ulam-stability of extremals for functionals represented in integral form is studied.

scholarly journals Hyers–Ulam stability of Euler’s equation

2011 ◽  
Vol 24 (9) ◽  
pp. 1539-1543 ◽  
Author(s):  
Dalia Sabina Cimpean ◽  
Dorian Popa
Keyword(s):  
Ulam Stability ◽  
Euler’S Equation ◽  
Euler's Equation

On the Unsteady Motion of a Viscous Hydromagnetic Fluid Contained in a Cylindrical Vessel

1966 ◽  
Vol 33 (4) ◽  
pp. 748-752
Author(s):  
R. N. Groves
Keyword(s):  
Operational Calculus ◽  
Integral Form ◽  
Hankel Transform ◽  
Unsteady Motion ◽  
Cylindrical Vessel ◽  
Axially Symmetric ◽  
Electrically Conducting ◽  
Special Cases ◽  
Constant Strength ◽  
The Laplace Transform

The problem of unsteady motion of an electrically conducting viscous liquid contained in a cylindrical vessel in the presence of an axially symmetric magnetic field of constant strength has been solved exactly by using concurrently two methods of operational calculus—the finite Hankel transform, and the Laplace transform. Results of these operations for general boundary conditions are presented in convolution integral form. The exact solutions of two special cases are presented in terms of tabulated functions, including those especially developed for the purposes of this paper. By examining the limiting cases of these special results, verification of results that have previously appeared in the literature and other interesting phenomena arise.

scholarly journals First case report of acute cholangitis secondary to Cronobacter sakazakii

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Syeda Sahra ◽  
Abdullah Jahangir ◽  
Neville Mobarakai ◽  
Allison Glaser ◽  
Ahmad Jahangir ◽  
...  
Keyword(s):  
Acute Cholangitis ◽  
Tube Placement ◽  
Cronobacter Sakazakii ◽  
First Case ◽  
Shunt Procedure ◽  
Intrahepatic Portosystemic Shunt ◽  
History Of ◽  
Cholecystostomy Tube ◽  
Percutaneous Cholecystostomy Tube ◽  
First Time

Abstract Introduction Cronobacter sakazakii is an opportunistic Gram-negative, rod-shaped bacterium which may be a causative agent of meningitis in premature infants and enterocolitis and bacteremia in neonates and adults. While there have been multiple cases of C. sakazakii infections, there have been no acute cholangitis cases reported in humans. Case presentation An 81-year-old male with a past medical history of basal cell carcinoma, alcoholic liver cirrhosis, transjugular intrahepatic portosystemic shunt procedure, complicated by staphylococcus bacteremia, pituitary tumor, glaucoma, and hypothyroidism presented to the emergency room with the complaint of diffuse and generalized 10/10 abdominal pain of 1 day’s duration. There was a concern for pancreatitis, acute cholangitis, and possible cholecystitis, and the patient underwent a percutaneous cholecystostomy tube placement. Blood cultures from admission and biliary fluid cultures both grew C. sakazakii. The patient was treated with a carbapenem and clinically improved. Conclusions The case study described a patient with multiple medical comorbidities that presented with C. sakazakii bacteremia and cholangitis. While this bacterium has been implicated in other infections, we believe this is the first time the bacteria is being documented to have caused acute cholangitis.

Optimization of thermal conductivity in composites loaded with the solid-solid phase-change materials

2018 ◽  
Vol 25 (6) ◽  
pp. 1157-1165
Author(s):  
Taoufik Mnasri ◽  
Adel Abbessi ◽  
Rached Ben Younes ◽  
Atef Mazioud
Keyword(s):  
Thermal Conductivity ◽  
Phase Change ◽  
Phase Change Materials ◽  
Solid Phase ◽  
Spherical Inclusions ◽  
First Case ◽  
The Matrix ◽  
Composite Conductivity ◽  
First Time

AbstractThis work focuses on identifying the thermal conductivity of composites loaded with phase-change materials (PCMs). Three configurations are studied: (1) the PCMs are divided into identical spherical inclusions arranged in one plane, (2) the PCMs are inserted into the matrix as a plate on the level of the same plane of arrangement, and (3) the PCMs are divided into identical spherical inclusions arranged periodically in the whole matrix. The percentage PCM/matrix is fixed for all cases. A comparison among the various situations is made for the first time, thus providing a new idea on how to insert PCMs into composite matrices. The results show that the composite conductivity is the most important consideration in the first case, precisely when the arrangement plane is parallel with the flux and diagonal to the entry face. In the present work, we are interested in exploring the solid-solid PCMs. The PCM polyurethane and a wood matrix are particularly studied.

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