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What is the gradient of a scalar function defined on a subspace of square matrices ?
We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier...
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Gradient Flow Exact Renormalization Group for Scalar Quantum Electrodynamics
Gradient Flow Exact Renormalization Group (GF-ERG) is a framework to define the renormalization group flow of Wilsonian effective action utilizing...
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Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations
Strain gradient plasticity has been the subject of extensive research in the past 40 years in order to model size effects in metal plasticity, on the...
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On trivial gradient hyperbolic Ricci and gradient hyperbolic Yamabe solitons
We provide conditions for a compact gradient hyperbolic Ricci and a compact gradient hyperbolic Yamabe soliton to be trivial, hence, the manifold to...
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Remarks on Gradient Yamabe Solitons
This note studies gradient Yamabe solitons realised as warped metrics. First, we prove that the potential function and the scalar curvature depend...
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Conformal geometry of complete quasi Yamabe gradient solitons
The purpose of this work is to study the conformal geometry of complete quasi Yamabe gradient solitons, which correspond to an interesting...
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Past-directed scalar field gradients and scalar-tensor thermodynamics
We refine and slightly enlarge the recently proposed first-order thermodynamics of scalar-tensor gravity to include gravitational scalar fields with...
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Directional Derivatives and Gradient
Let a real-valued function f of two real variables of class C1 be given. A vector, called the gradient of the function, whose components are the...
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\(\mathcal {M}_1(N)\) : Map**s for Velocity-Scalar and Position-Scalar Pdfs
The CCK map** method is extended to velocity-scalar Pdfs in the spatial description and to position- scalar Pdfs in the material description. The...
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Skin Friction from Surface Scalar Visualizations
This chapter describes extraction of a skin friction field from surface scalar visualizations with pressure sensitive paint (PSP) as an oxygen sensor...
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Properties of Warped Product Gradient Yamabe Solitons
In this paper, we study gradient Yamabe solitons realized as warped product manifolds. We apply the maximum principle to find lower bound estimates...
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Notes on m-quasi Yamabe gradient solitons
We derive a divergence formula for an m -quasi Yamabe gradient soliton with finite m , and use it to give a short proof of the result “A compact m -quasi...
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Collective Gradient Following with Sensory Heterogeneous UAV Swarm
In this paper, we present a new method for a swarm to collectively sense and follow a gradient in the environment. The agents in the swarm only rely...
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Scalar Potentials and Applications
Vector- and scalar-potential-based methods for aiding in the solution of Maxwell equations are discussed. In particular, potential-based methods for...
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Existence of gradient CKV and gradient conformally stationary LRS spacetimes
In this work, we study the existence of gradient (proper) CKVs in locally rotationally symmetric spacetimes (LRS), those CKVs in the space spanned by...
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Diabetes Risk Prediction Through Fine-Tuned Gradient Boosting
Diabetes, a chronic metabolic disease with a rising global prevalence, significantly impacts individuals’ health. Diabetes increases a person’s risk...
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Cosmic Acceleration, Scalar Fields, and Observations
Conditions for accelerated expansion of Friedmann–Robertson–Walker space–time are analyzed. Connection of this scenario with present–day observations...