scholarly journals A UNIQUE PERFECT POWER DECAGONAL NUMBER

2021 ◽  
pp. 1-5
Author(s):  
PHILIPPE MICHAUD-RODGERS
Keyword(s):  
All Solutions ◽  
Modular Method

Abstract Let $\mathcal {P}_s(n)$ denote the nth s-gonal number. We consider the equation $$ \begin{align*}\mathcal{P}_s(n) = y^m \end{align*} $$ for integers $n,s,y$ and m. All solutions to this equation are known for $m>2$ and $s \in \{3,5,6,8,20 \}$ . We consider the case $s=10$ , that of decagonal numbers. Using a descent argument and the modular method, we prove that the only decagonal number greater than 1 expressible as a perfect mth power with $m>1$ is $\mathcal {P}_{10}(3) = 3^3$ .

Exogeneous factors are not necessary in attachment, spreading and polarization of hela cells

1978 ◽  
Vol 36 (2) ◽  
pp. 310-311
Author(s):  
W. Liebrich
Keyword(s):  
Hela Cells ◽  
Calf Serum ◽  
Glass Tube ◽  
Serum Free Medium ◽  
Nacl Solution ◽  
Free Medium ◽  
Minimum Essential Medium ◽  
Serum Free ◽  
All Solutions ◽  
Glass Support

HeLa cells were grown for 2-3 days in EAGLE'S minimum essential medium with 10% calf serum (S-MEM; Seromed, München) and then incubated for 24 hours in serum free medium (MEM). After detaching the cells with a solution of 0. 14 % EDTA and 0. 07 % trypsin (Difco, 1 : 250) they were suspended in various solutions (S-MEM = control, MEM, buffered salt solutions with or without Me++ions, 0. 9 % NaCl solution) and allowed to settle on glass tube slips (Leighton-tubes). After 5, 10, 15, 20, 25, 30, 1 45, 60 minutes 2, 3, 4, 5 hours cells were prepared for scanning electron microscopy as described by Paweletz and Schroeter. The preparations were examined in a Jeol SEM (JSM-U3) at 25 KV without tilting.The suspended spherical HeLa cells are able to adhere to the glass support in all solutions. The rate of attachment, however, is faster in solutions without serum than in the control. The latter is in agreement with the findings of other authors.

Block-modular method for the construction of oil and gas facilities

2019 ◽  
Vol 12 ◽  
pp. 69-73
Author(s):  
I.P. Kozhushkov ◽  
◽  
A.P. Smirnov ◽  
Keyword(s):  
Oil And Gas ◽  
Modular Method

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

scholarly journals Simplified and improved criteria for oscillation of delay differential equations of fourth order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. Moaaz ◽  
A. Muhib ◽  
D. Baleanu ◽  
W. Alharbi ◽  
E. E. Mahmoud
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Oscillatory Behavior ◽  
Interesting Point ◽  
All Solutions ◽  
Special Cases ◽  
Delay Differential ◽  
Noncanonical Operator

AbstractAn interesting point in studying the oscillatory behavior of solutions of delay differential equations is the abbreviation of the conditions that ensure the oscillation of all solutions, especially when studying the noncanonical case. Therefore, this study aims to reduce the oscillation conditions of the fourth-order delay differential equations with a noncanonical operator. Moreover, the approach used gives more accurate results when applied to some special cases, as we explained in the examples.

scholarly journals A COVID-19 Lockdown Tabletop Exercise in New Taipei City, Taiwan

2021 ◽  
pp. 1-19
Author(s):  
I-Tien Lo ◽  
Ching-Yuan Lin ◽  
Ming-Tai Cheng
Keyword(s):  
Policy Making ◽  
Large City ◽  
Strategic Plan ◽  
Government Control ◽  
Subject Knowledge ◽  
All Solutions ◽  
Taipei City ◽  
Returning To Work ◽  
Three Stages ◽  
Stage 1

Abstract Objectives: This exercise aimed to validate New Taipei City’s strategic plan for a city lockdown in response to COVID-19. The main goal of all solutions was the principle of “reducing citizen activity and strengthening government control”. Methods: We created a suitable exercise, and creating 15 hypothetical situations for three stages. All participating units designed and proposed policy plans and execution protocols according to each situation. Results: In the course of the exercise, many existing policies and execution protocols were validated to address. Situations occurring in Stage 1, when the epidemic was spreading to the point of lockdown preparations, approaches to curb the continued spread of the epidemic in Stage 2, and returning to work after the epidemic is controlled and lockdown is lifted in Stage 3. Twenty response units participated in the exercise. Although favourable outcomes were obtained, the evaluators provided comments suggesting further improvements. Conclusions: Our exercise demonstrated a successful example to help policy making and revision in a large city over 4 million population during COVID-19 pandemic. It also enhanced participants’ subject knowledge and familiarity with the implementation of a city lockdown. For locations intending to go into lockdown, similar tabletop exercises are an effective verification option.

scholarly journals On the Ternary Exponential Diophantine Equation Equating a Perfect Power and Sum of Products of Consecutive Integers

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1813
Author(s):  
S. Subburam ◽  
Lewis Nkenyereye ◽  
N. Anbazhagan ◽  
S. Amutha ◽  
M. Kameswari ◽  
...  
Keyword(s):  
Positive Integer ◽  
Diophantine Equation ◽  
Upper Bound ◽  
Exponential Diophantine Equation ◽  
Research Article ◽  
All Solutions ◽  
Sum Of Products ◽  
Consecutive Integers ◽  
Sums Of Products ◽  
Positive Integers

Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality n= 19,736 to obtain all solutions (x,y,n) of the equation for the fixed positive integers k≤10. In this paper, we improve the bound as n≤ 10,000 for the same case k≤10, and for any fixed general positive integer k, we give an upper bound depending only on k for n.

scholarly journals Mass and spin for classical strings in dS3

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Klaas Parmentier
Keyword(s):  
Black Hole ◽  
Evolution Equation ◽  
Cosmic Strings ◽  
Center Of Mass ◽  
Open String ◽  
Conserved Quantities ◽  
Numerical Example ◽  
All Solutions

Abstract We demonstrate that all rigidly rotating strings with center of mass at the origin of the dS3 static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser’s algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin < 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.

scholarly journals Comparison of the Cerumenolytic Activities of New and Currently Used Agents

2021 ◽  
pp. 014556132098606
Author(s):  
Nguyen Quynh Anh ◽  
Pawin Numthavaj ◽  
Thongchai Bhongmakapat
Keyword(s):  
Salicylic Acid ◽  
Sodium Bicarbonate ◽  
Potassium Hydroxide ◽  
Glycolic Acid ◽  
Statistical Significance ◽  
In Vitro Study ◽  
Distilled Water ◽  
Moderate Amount ◽  
All Solutions

Objectives: This study compared the cerumen dissolution activities of 7.5% sodium bicarbonate, 5% potassium hydroxide, 10% lactic acid, 3% salicylic acid, 10% glycolic acid, and distilled water. Methods: An in vitro study was conducted with 36 cerumen samples. The cerumenolytic activities of the 6 agents were assessed by recording the degree of cerumen disintegration using digital photography at 15 minutes, 30 minutes, 1 hour, 2 hours, and 12 hours. The undissolved cerumen that remained after 12 hours was removed from the solutions and weighed after drying. Results: Potassium hydroxide showed the fastest cerumenolytic activity, dissolving a moderate amount of cerumen at 30 minutes, while glycolic acid and salicylic acid caused no visible changes in the cerumen samples. Samples treated with potassium hydroxide and sodium bicarbonate exhibited higher degrees of disintegration compared to samples treated with distilled water (odds ratio and 95% CI: 273.237 [0.203-367 470.4] and 1.129 [0.002-850.341], respectively). The greatest reduction in cerumen weight was associated with the use of sodium bicarbonate; however, this result did not reach statistical significance. Conclusions: Among the solutions tested, 5% potassium hydroxide showed the fastest dissolution activity, yielding moderate disintegration within only 30 minutes. In terms of residual cerumen weight within 12 hours, all solutions exhibited equivalent effectiveness in the disintegration of cerumen.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

scholarly journals The holographic conformal manifold of 3d $$ \mathcal{N} $$ = 2 S-fold SCFTs

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Nikolay Bobev ◽  
Friðrik Freyr Gautason ◽  
Jesse van Muiden
Keyword(s):  
String Theory ◽  
Three Dimensional ◽  
Parameter Family ◽  
Global Symmetry ◽  
Maximal Supergravity ◽  
All Solutions ◽  
Operator Spectrum ◽  
Type Iib String Theory ◽  
Two Parameter

Abstract We employ a non-compact gauging of four-dimensional maximal supergravity to construct a two-parameter family of AdS4 J-fold solutions preserving $$ \mathcal{N} $$ N = 2 supersymmetry. All solutions preserve $$ \mathfrak{u} $$ u (1) × $$ \mathfrak{u} $$ u (1) global symmetry and in special limits we recover the previously known $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{u} $$ u (1) invariant $$ \mathcal{N} $$ N = 2 and $$ \mathfrak{su} $$ su (2) × $$ \mathfrak{su} $$ su (2) invariant $$ \mathcal{N} $$ N = 4 J-fold solutions. This family of AdS4 backgrounds can be uplifted to type IIB string theory and is holographically dual to the conformal manifold of a class of three-dimensional S-fold SCFTs obtained from the $$ \mathcal{N} $$ N = 4 T [U(N)] theory of Gaiotto-Witten. We find the spectrum of supergravity excitations of the AdS4 solutions and use it to study how the operator spectrum of the three-dimensional SCFT depends on the exactly marginal couplings.

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