Not to be confused with the Assistant endpoint, this role is usually the model’s response to the user. It provides the output based on the system’s instructions, the user’s input, and previous context. You can write your own responses for this role, further aiding the model to give ...
This article has been updated Abstract The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy–momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation of the f(R,GμνTμν...
such a n-adapted base is holonomic and we can write it as a partial derivative \(\partial _{\alpha }\) with \(n_{i}^{a}=0.\) in curved local coordinates, the coefficients \(n_{j}^{a}\) may be nontrivial even all \(w_{\alpha \beta }^{\gamma }=0\) and we may chose...
We assume the (high mechanical quality) conditions \({\mathcal{Q}}=\omega /\gamma \gg 1\), as it is the case experimentally, so that the Brownian noise operators can de facto be treated as uncoloured noise and we can write \(\langle {\xi }_{j}(t){\xi }_{j}({t}^{\prime...
We may now write down the bulk geometry with a cosmic brane homologous to the first disk A1: ds2d þ 1 ¼ dr2 f ðrÞ þ f ðrÞdt2 þ r2 ðdr2 þ sinh2rdO2d À 2Þ; ð32Þ where for Einstein gravity we have f ðrÞ ¼ r2 À 1À rhd À...
Write an SQL query builder in 150 lines of Python! 20 minute read This is the fourth article in a series about writing my own SQL query builder. Today, we'll rewrite it from scratch, explore API design, learn when to be lazy, and look at worse and better ways of doing things –...
To apply the conformal blocks technique one has to rewrite local solutions obtained in the previous section in the conformal form. This should be done in every domain where the solution is defined because a global solution is obtained by gluing all patches together. Before doing this we write ...
So we can write the most general ansatz as(5)ds2=−h(r)dt2+dr2f(r)+r2dΩ22,ϕ=ϕ(r),A=Φ(r)dt, in which the Φ(r) is the U(1) gauge field potential. By solving the Maxwell equation ∇νFνμ=0, the field potential Φ can be expressed as(6)Φ′=4Qr2hf, where...
In addition, one writes the properties of ψL,n and ψR,n as i γμ∂μψL,n = mψRn, i γμ∂μψR,n = mψL,n, (36) and γ 4ψL,n = −ψL,n, γ 4ψR,n = ψR,n. (37) Making use of the chiral decomposition as well as the above properties, we obtain ...
In this paper, a new generalised gravity-matter coupled theory of gravity is presented. This theory is constructed by assuming an action with an arbitrary functionf(T,B,Lm)which depends on the scalar torsionT, the boundary termB=∇μTμand the matter LagrangianLm. Since the function depends...