Conception of a Web Operation System for Processing Petroleum Related Drilling Data: A Focus on Pre-Salt Real-Time Automation and Optimization

Petroleum and Natural Gas still represent a considerable share in terms of energy consumption in the current global matrix, so that its exploration/exploitation is present in the market and driving activities in locations of specific complexities, as the ones along unconventional hydrocarbon resources from the Brazilian pre-salt. The daily cost of well drilling under harsh conditions can exceed US $1 million a day, turning any type of downtime or necessary maintenance during the activities to be very costly, moment in which processes optimization starts to be a key factor in costs reduction. Thus, new technologies and methods in terms of automating and optimizing the processes may be of great advantages, having its impact in total related project costs. In this context, the goal of this research is to allow a computation tool supporting achieving a more efficient drilling process, by means of drilling mechanics parameters choosiness aiming rate of penetration (ROP) maximization and mechanic specific energy (MSE) minimization. Conceptually, driven by the pre-operational drilling test curve trends, the proposed system allows it to be performed with less human influences and being updateable automatically, allowing more precision and time reduction by selecting optimum parameters. A Web Operating System (Web OS) was designed and implemented, running in online servers, granting accessibility to it with any device that has a browser and internet connection. It allows processing the drilling parameters supplied and feed into it, issuing outcomes with optimum values in a faster and precise way, allowing reducing operating time.

EXISTENCE OF A GROUND STATE SOLUTION FOR THE CHOQUARD EQUATION WITH NONPERIODIC POTENTIALS

We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.

Dynamics of a Reaction-diffusion-ODE System in a Heterogeneous Media

The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this paper.We first show that there exist both continuous and discontinuous stationary solutions.Then a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate condition.In addition,we demonstrate the influences of the diffusion coefficient on stationary solutions.The results we obtained are based on the super-/sub-solution method and the generalized mountain pass theorem.Finally,some numerical simulations are given to illustrate the theoretical results.

Attractor for the Extensible Beam Equation with Nonlocal Weak Damping on Time–Dependent Space

In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infinity.Within the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed estimates.The results obtained essentially improve and complete some previous works.

On the centers of quantum groups of A_n-type

Let g be the finite dimensional simple Lie algebra of type A_n, and let U = U_q(g,Λ)and U= U_q(g,Q)be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U = U_q(g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U = U_q(g,Λ) and U = U_q(g,Q).

Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way.In order to understand the topological properties of the self-similar network,we have done a lot of research in this field.Firstly,according to the symmetry feature of the self-similar network,we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then,we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally,we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.

Holder Continuity of Spectral Measures for the Finitely Differentiable Quasi-Periodic Schrodinger Operators

In the present paper,we prove the 1/2-Holder continuity of spectral measures for the C^k Schrodinger operators.This result is based on the quantitative almost reducibility and an estimate for the growth of the Schrodinger cocycles in[5].

Twisted Whittaker modules over U_(q)(gl_(n+1))

As is well known,the classical nonsingular Whittaker modules over quantum groups cannot be defined for the non-A1 type.In this paper,by choosing different generators for the quantum group U_(q)(gl_(n+1)),we introduce and study the twisted Whittaker modules over U_(q)(gl_(n+1)).We classify all the simple twisted Whittaker modules with nonsingular Whittaker functions.This agrees with Kostant’s results on Whittaker modules for the simple complex Lie algebras sln+1 as q approaches 1.

Optimizing COVID-19 vaccination programs during vaccine shortages

During the ongoing COVID-19 pandemic, vaccine shortages occur due to various types of constraints, including interruptions in production/supply, higher-than-expected demands, and a lack of resources such as healthcare capacity to administer vaccines. Scientifically informed epidemic models have been utilized as pivotal tools to optimize the immunization programs subject to vaccine shortages. The current paper reviews modelling methods to optimize the allocation strategies of vaccines with differential efficacies by using various model-based outcome measures. The models reviewed in this study are expected to be adopted and extended to make contributions on policy development for disease control under the vaccine shortage scenario.

A critical Trudinger-Moser inequality involving a degenerate potential and nonlinear Schrodinger equations

The classical critical Trudinger-Moser inequality in R^(2)under the constraint∫_(R_(2))(|▽u|^(2)+|u|^(2))dx≤1 was established through the technique of blow-up analysis or the rearrangement-free argument:for anyτ>0,it holds that sup u∈H^(1)(r^(2)fR^(2)(τ|U|^(2)+|▽u|^(2)dx≤1∫_(R^(2)(E^4π|u|^(2)-1)dx≤C(τ)<+∞)))and 4πis sharp.However,if we consider the less restrictive constraint∫_(R_(2))(|▽u|^(2)+|u|^(2))dx≤1,where V(x)is nonnegative and vanishes on an open set in R^(2),it is unknown whether the sharp constant of the Trudinger-Moser inequality is still 4π.The loss of a positive lower bound of the potential V(x)makes this problem become fairly nontrivial.The main purpose of this paper is twofold.We will first establish the Trudinger-Moser inequality sup u∈H^(1)(r^(2)fR^(2)(τ|U|^(2)+|▽u|^(2)dx≤1∫_(R^(2)(E^4π|u|^(2)-1)dx≤C(τ)<+∞)))when V is nonnegative and vanishes on an open set in R^(2).As an application,we also prove the existence of ground state solutions to the following Sciridinger equations with critical exponeitial growth:-Δu+V(x)u=f u)in R^(2),(0.1)where V(x)≥0 and vanishes on an open set of R^(2)and f has critical exponential growth.Having a positive constant lower bound for the potential V(x)(e.g.,the Rabinowitz type potential)has been the standard assumption when one deals with the existence of solutions to the above Schrodinger equations when the nonlinear term has the exponential growth.Our existence result seems to be the first one without this standard assumption.

Majid conjecture: quantum Kac-Moody algebras version

Based on the n-fold tensor product version of the generalized double-bosonization construction,we prove the Majid conjecture of the quantum Kac-Moody algebras version.Particularly,we give explicitly the double-bosonization type-crossing constructions of quantum Kac-Moody algebras for affine types G(1)2,E(1)6,and Tp,q,r,and in this way,we can recover generators of quantum Kac-Moody algebras with braided groups defined by R-matrices in the related braided tensor category.This gives us a better understanding for the algebra structures themselves of the quantum Kac-Moody algebras as a certain extension of module-algebras/module-coalgebras with respect to the related quantum subalgebras of finite types inside.

Classification on irreducible Whittaker modules over quantum group Uq(sl3,∧)

We define the Whittaker modules over the simply-connected quantum group U_(q)(sl3,∧),where A is the weight lattice of Lie algebra sl3.Then we completely classify all those simple ones.Explicitly,a simple Whittaker module over U_(q)(sl3,∧)is either a highest weight module,or determined by two parameters z∈C andγ∈C^(*)(up to a Hopf automorphism).

The Polynomial Modules over Quantum Group U_(q)(sl3)

Let g be a finite dimensional complex simple Lie algebra with Cartan subalgebraη.Then C[η]has a g-module structure if and only if g is of type A or of type C;this is called the polynomial module of rank one,In the quantum version,the rank one polynomial modules over U_(q)(sl_(2))have been classified.In this paper,we prove that the quantum group U_(q)(sl_(3))has no rank one polynomial module.

Trudinger-Moser Type Inequality Under Lorentz-Sobolev Norms Constraint

In this paper,we are concerned with a sharp fractional Trudinger-Moser type inequality in bounded intervals of IR under the Lorentz-Sobolev norms constraint.For any 1<q<∞andβ≤(√π)q'≡βq'q'=q/q-1,we obtain u∈Н1/2,2(I),^sup||(-△)1/4u||2,q≤1^(∫Ieβ|u(x)|q'dx≤c0|I|),andβq is optimal in the sense that u∈Н1/2,2(I),^sup||(-△)1/4u||2,q≤1^(∫Ieβ|u(x)|q'dx+∞),for anyβ>βq.Furthermore,when q is even,we obtain u∈Н1/2,2(I),^sup||(-△)1/4u||2,q≤1^(∫Ih(u)eβq|u(x)|q')dx≤+∞),for any function h:[0,∞→[0,∞)with lim t→∞h(t)=∞.As for the key tools of proof,we use Green functions for fractional Laplace operators and the rearrangement of a convolution to the rearrangement of the convoluted functions.

Finite dimensional modules over quantum toroidal algebras

For all generic q∈C^∗,when g is not of type A1;we prove that the quantum toroidal algebra Uq(gtor)has no nontrivial finite dimensional simple module.