A monotone iterative method is applied to show the existence of an extremal solution for a nonlinear system involving the right-handed Riemann–Liouville fractional derivative with nonlocal coupled ...integral boundary conditions. Two comparison results are established. As an application, an example is presented to demonstrate the efficacy of the main result.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Since an interesting functional by P.L. Chebyshev was presented in the year 1882, many results, which are called Chebyshev-type inequalities, have been established. Some of these inequalities were ...obtained by using fractional integral operators. Very recently, a new variant of the fractional conformable integral operator was introduced by Jarad et al. Motivated by this operator, we aim at establishing novel inequalities for a class of differentiable functions, which are associated with Chebyshev’s functional, by employing a fractional conformable integral operator. We also aim at showing important connections of the results here with those including Riemann–Liouville fractional and classical integrals.
Left ventricular assist device (LVAD) implantation is an accepted therapy for patients with end-stage heart failure. Post-operative right ventricular failure (RVF) still remains a major cause of ...morbidity and mortality in these patients. This study sought to identify echocardiography parameters to select patients with high risk of RVF after LVAD implantation.
Prospectively collected pre-operative transesophageal echocardiography (TEE) and clinical data were evaluated in patients pre-selected for isolated LVAD or biventricular assist device (BiVAD) implantation. According to prevalence of RVF during the first post-operative 48 hours, patients were divided into those who developed RVF (isolated LVAD with RVF) and those who did not (isolated LVAD without RVF). Echocardiographic parameters for RV geometry, RV function, LV geometry, and the RV-to-LV end-diastolic diameter ratio (R/L ratio) were evaluated. For identification of the optimal cutoff of R/L ratio, receiver operating characteristics curves were constructed.
An isolated LVAD was implanted in 115 patients and BiVAD in 22 patients. RVF developed in 15 patients (13%) after isolated LVAD implantation. The R/L ratio was markedly increased in the isolated LVAD with RVF and BiVAD groups compared with the isolated LVAD without RVF group. According to the receiving operating curve, the cutoff for the R/L ratio to predict RVF was 0.72. The odds ratio that RVF will develop is 11.4 in patients with an R/L ratio >0.72 (p = 0.0001).
Increased R/L ratio successfully identifies patients with high risk of RVF after isolated LVAD implantation. Beyond standard measurements of RV function, the consideration of R/L ratio may be useful to improve risk stratification in patients before isolated LVAD implantation.
•A novel single-end distance protection scheme for HVDC lines is proposed.•This protection is based on the linear distribution of low frequency voltage signals along the line.•Principles of mho relay ...are improved and applied in the new protection.•An internal fault can be detected if the measure voltage is opposite in sign with the compensating voltage.•Compared with other single-end HVDC line protections, this novel method has numerous merits.
HVDC transmission system is becoming increasingly desirable for its obvious technical and environmental advantages. A novel single-end distance protection scheme for HVDC lines is proposed in this paper. It is based on the linear distribution of low frequency voltage signals between the relay point and setting point. An internal fault can be detected if the low-pass filtered measure voltage is opposite in sign with the compensating voltage at the setting point, which can be calculated with the R-L differential-equation algorithm. To find a tradeoff between operating speed and accuracy, the protection is divided into K zones, each of which has different protection scopes and cut-off frequencies. A two-terminal HVDC system and a multi-infeed HVDC system are respectively built in EMTDC. Comprehensive simulation results have indicated that the proposed protection scheme has satisfactory operation performance and will be not influenced by system topologies or parameters. Besides, it is not sensitive to noises or voltage levels. Compared with many other single-end protections for HVDC lines, this novel distance protection has clear setting principles, lower sampling frequency, smaller calculation amount and faster operating speed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
16.
Wormhole solutions in f(R,Lm) gravity Solanki, Raja; Hassan, Zinnat; Sahoo, P.K.
Chinese journal of physics (Taipei),
October 2023, 2023-10-00, Volume:
85
Journal Article
Peer reviewed
In this work, we intend to explore wormhole geometries in the framework of f(R,Lm) gravity. We derive the field equations for the generic f(R,Lm) function by assuming the static and spherically ...symmetric Morris–Thorne wormhole metric. Then we consider two non-linear f(R,Lm) model, specifically, f(R,Lm)=R2+Lmα and f(R,Lm)=R2+(1+λR)Lm, where α and λ are free model parameters. We obtain the wormhole solutions by assuming three cases, namely, a linear barotropic EoS, anisotropic EoS, and isotropic EoS corresponding to model I. We observe that for both barotropic and anisotropic cases, the corresponding wormhole solutions obey the flaring-out condition under asymptotic background, while for the isotropic case, the shape function does not follow the flatness condition. Also, we find that the null energy condition exhibits negative behavior in the vicinity of the throat. Further, we consider two different shape functions to investigate the behavior of model II. We find some constraints on the model parameter for which the violation of the null energy condition exhibits. Finally, we employ the volume integral quantifier to calculate the amount of exotic matter required near the wormhole throat for both models. We conclude that the modification of standard GR can efficiently minimize the use of exotic matter and provide stable traversable wormhole solutions.
Display omitted Behavior of the shape function (barotropic EoS) and 3D embedding diagram corresponding to the f(R,Lm)=R2+Lmαmodel.
•We derive the field equations for the generic f(R,Lm) function.•We investigate non-linear functionals f(R,Lm)=R2+Lmα and f(R,Lm)=R2+(1+λR)Lm.•We use the VIQ technique to calculate the amount of exotic matter near the throat.•We found that the modified GR could provide stable wormhole solutions.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Abstract In this work, we have explored wormhole (WH) solutions in F ( R , L m ) gravity by assuming the Morris–Thorne WH metric and F ( R , L m ) = R 2 + ( 1 + γ R ) L m , where γ is the free model ...parameter. We determined the WH solutions by utilizing two newly developed shape functions (SF) that satisfy all basic conditions for a WH’s physical validity. We also observe that the null energy condition (NEC) behaves negatively. Finally, for both models, we use the volume integral quantifier ( V I Q ) and Tolman–Oppenheimer–Volkoff (TOV) equation to determine how much exotic matter is needed near the WH throat and the stability of the WH. The extensive detailed discussions of the matter components have been done via graphical analysis. The obtained WH geometries meet the physically acceptable conditions for a stable wormhole.
•A graph G=(V,E) is C-probe if V(G) can be partitioned into two sets: non-probesN and probesP, where N is an independent set and new edges may be added between some non-probe vertices such that the ...resulting graph is in the class C.•In this case, we say that (N,P) is a C-probe partition of G. In the Unpartitioned Probe problem for a graph class C we are given a graph G and asked whether G has a C-probe partition.•A graph G=(V,E) is an (r,ℓ)-graph when V can be partitioned into (S1,S2,…,Sr,K1,K2,…,Kℓ) such that S1,S2,…,Sr are independent sets, and K1,K2,…,Kℓ are cliques.•A graph G is well-covered if every maximal independent set is also maximum.•In this paper, we study the complexity of the Unpartitioned Probe problem for the class of (r,ℓ)-well-covered graphs. We classify all but the (2,0) and (1,2) cases.
Let C be a class of graphs. A graph G=(V,E) is C-probe if V(G) can be partitioned into two sets: non-probesN and probesP, where N is an independent set and new edges may be added between some non-probe vertices such that the resulting graph is in the class C. In this case, we say that (N,P) is a C-probe partition of G. In the Unpartitioned Probe problem for a graph class C we are given a graph G and asked whether G has a C-probe partition, i.e., such a problem consist of recognizing the class of C-probe graphs. A graph G=(V,E) is an (r,ℓ)-graph when V can be partitioned into (S1,S2,…,Sr,K1,K2,…,Kℓ) such that S1,S2,…,Sr are independent sets, and K1,K2,…,Kℓ are cliques. A graph G is well-covered if every maximal independent set is also maximum, and it is (r,ℓ)-well-covered if it is well-covered as well as an (r,ℓ)-graph. In this paper, we study the complexity of the Unpartitioned Probe problem for the class of (r,ℓ)-well-covered graphs. We classify all but the (2,0) and (1,2) cases.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
19.
On the complexity of coloring (r,ℓ)‐graphs Alves, Matheus S. D.; Nascimento, Julliano R.; Souza, Uéverton S.
International transactions in operational research,
November 2021, Volume:
28, Issue:
6
Journal Article
Peer reviewed
An (r,ℓ)‐graph is a graph that can be partitioned into r independent sets and ℓ cliques. In the Graph Coloring problem, we are given as input a graph G, and the objective is to determine the minimum ...integer k such that G admits a proper vertex k‐coloring. In this work, we describe a Poly versus NP‐hard dichotomy of this problem regarding the parameters r and ℓ of (r,ℓ)‐graphs, which determine the boundaries of the NP‐hardness of Graph Coloring for such classes. We also analyze the complexity of the problem on (r,ℓ)‐graphs under the parameterized complexity perspective. We show that given a (2, 1)‐partition S1,S2,K1 of a graph G, finding an optimal coloring of G is NP‐complete even when K1 is a maximal clique of size 3; XP but W1‐hard when parameterized by min{|S1|,|S2|}; fixed‐parameter tractable (FPT) and admits a polynomial kernel when parameterized by max{|S1|,|S2|}. Besides, concerning the case where K1 is a maximal clique of size 3, a P versus NPh dichotomy regarding the neighborhood of K1 is provided; furthermore, an FPT algorithm parameterized by the number of vertices having no neighbor in K1 is presented.
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FZAB, GIS, IJS, IZUM, KILJ, NLZOH, NUK, OILJ, PILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
Abstract
In this article, we investigate the observed cosmic acceleration in the framework of a cosmological
f
(
R
,
L
m
) model dominated by bulk viscous matter in an anisotropic background. We ...consider the locally rotationally symmetric Bianchi type I metric and derive the Friedmann equations that drive the gravitational interactions in
f
(
R
,
L
m
) gravity. Further, we assume the functional form
f
(
R
,
L
m
)
=
R
2
+
L
m
α
, where
α
is a free model parameter, and then find the exact solutions of field equations corresponding to our viscous matter dominated model. We incorporate the updated H(z) data and the Pantheon data to acquire the best-fit values of parameters of our model by utilizing the
χ
2
minimization technique along with the Markov Chain Monte Carlo random sampling method. Further, we present the behavior of physical parameters that describe the Universe’s evolution phase, such as density, effective pressure and EoS parameters, skewness parameter, and the statefinder diagnostic parameters. We find that the energy density indicates expected positive behavior, whereas the negative behavior of bulk viscous pressure contributes to the Universe’s expansion. The effective EoS parameter favors the accelerating phase of the Universe’s expansion. Moreover, the skewness parameter shows the anisotropic nature of spacetime during the entire evolution phase of the Universe. Finally, from the statefinder diagnostic test, we found that our cosmological
f
(
R
,
L
m
) model lies in the quintessence region, and it behaves like a de-Sitter universe in the far future. We analyze different energy conditions in order to test the consistency of the obtained solution. We find that all energy conditions except strong energy condition (SEC) show positive behavior, while the violation of SEC favors the recently observed acceleration with the transition from decelerated to an accelerated epoch of the Universe’s expansion in the recent past.
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