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In this note we briefly survey and propose some open problems related to isoparametric theory.

Intrinsic image decomposition aims to separate the surface reflectance and the effects from the illumination given a single photograph. Due to the complexity of the problem, most prior works assume a single-color illumination and a…

While large language models (LLMs) have demonstrated remarkable capabilities across a range of downstream tasks, a significant concern revolves around their propensity to exhibit hallucinations: LLMs occasionally generate content that…

It is shown that some problems connected with dark matter and dark energy can be solved in the framework of the byuon theory

This paper gives a survey of the progress on the minimal genus problem since Lawson's survey.

We propose a novel Retinex image-decomposition network that can be trained in a self-supervised manner. The Retinex image-decomposition aims to decompose an image into illumination-invariant and illumination-variant components, referred to…

Visualization design study research methodologies emphasize the need for reflection to generate knowledge. And yet, there is very little guidance in the literature specifying what reflection in the context of design studies actually…

Gravitational lenses can provide crucial information on the geometry of the Universe, on the cosmological scenario of formation of its structures as well as on the history of its components with look-back time. In this review, I focus on…

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…

The nature of dark matter and the origin of the baryon asymmetry are two of the deepest mysteries of modern particle physics. In the absence of hints regarding a possible solution to these mysteries, many approaches have been developed to…

We study the existence and uniqueness of solutions of a nonlinear integro-differential problem which we reformulate introducing the notion of the decreasing rearrangement of the solution. A dimensional reduction of the problem is obtained…

Due to the low accuracy of object detection and recognition in many intelligent surveillance systems at nighttime, the quality of night images is crucial. Compared with the corresponding daytime image, nighttime image is characterized as…

In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.

The phenomenon of the Dark matter baffles the researchers: the underlying dark particle has escaped so far the detection and its astrophysical role appears complex and entangled with that of the standard luminous particles. We propose that,…

The identity of dark matter is one of the key outstanding problems in both particle and astrophysics. In this thesis, I review some candidates of dark matter, especially WIMPs (weakly interacting massive particles) which is one of the best…

The status of the solar neutrino problem is reviewed. Attempts to explain the observed deficit and spectral distortion, both by astrophysical and particle physics methods, are described. It is argued that the comparison of all experiments…

We review the state of research on empathy in natural language processing and identify the following issues: (1) empathy definitions are absent or abstract, which (2) leads to low construct validity and reproducibility. Moreover, (3)…

The Plateau's problem seeks to determine a surface of minimal area which spans a given boundary. It is widely studied for its varied mathematical formulations, applications and relevance to physical models such as soap films. We revisit the…

The smallness of the cosmological constant is one of the basic problems in particle physics and cosmology. Various attempts have been made to explain this mystery, but no satisfactory solution has been found yet. The appearance of extra…

The apparent fine-tuning of several fundamental parameters that determine the properties of our Universe and make it hospitable to life is sometimes used as an argument for God from design. I review the concept of cosmic fine-tuning and…