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Yong Yao

Publications and source records attributed to Yong Yao.

18 recordsLinked to original sources
arXiv2026

Majorization and Inequalities among Complete Homogeneous Symmetric Functions

Inequalities among symmetric functions are fundamental in various branches of mathematics, thus motivating a systematic study of their structure. Majorization has been shown to characterize inequalities among commonly used symmetric functions, except for complete homogeneous symmetric functions (shortened as CHs). In 2011, Cuttler, Greene, and Skandera posed a natural question: Can majorization also characterize inequalities among CHs? Their work demonstrated that majorization characterizes inequalities among CHs up to degree 7 and suggested exploring its validity for higher degrees. In this paper, we show that, for every degree greater than 7, majorization does not characterize inequalities among CHs.

cs.SC↗
arXiv2025

Scientific Objectives of the Xue-shan-mu-chang 15-meter Submillimeter Telescope

Submillimeter astronomy is poised to revolutionize our understanding of the Universe by revealing cosmic phenomena hidden from optical and near-infrared observations, particularly those associated with interstellar dust, molecular gas, and star formation. The Xue-shan-mu-chang 15-meter submillimeter telescope (XSMT-15m), to be constructed at a premier high-altitude site (4813 m) in Qinghai, China, marks a major milestone for Chinese astronomy, establishing the China mainland's first independently developed, world-class submillimeter facility. Equipped with state-of-the-art instruments, XSMT-15m will address a diverse range of frontier scientific questions spanning extragalactic astronomy, Galactic structure, time-domain astrophysics, and astrochemistry. In synergy with current and forthcoming observatories, XSMT-15m will illuminate the formation and evolution of galaxies, unravel the physical and chemical processes shaping the interstellar medium, and explore transient phenomena in the submillimeter regime. These capabilities will advance our understanding across extragalactic astronomy, Galactic ecology, astrochemistry, and time-domain astrophysics, inaugurating a new era for submillimeter research in China and the northern hemisphere.

astro-ph.GA↗
arXiv2025

Inequalities among Symmetric Polynomial Functions: Counter-examples and New Conjectures

Inequalities among symmetric polynomial functions are fundamental questions in mathematics and have various applications in science and engineering. This paper investigates a beautiful and inspiring conjecture, proposed by Cuttler, Greene and Skandera in 2011, on inequalities among the complete homogeneous symmetric polynomial function $H_{n,λ}$: It states that the inequality $H_{n,λ}\leq H_{n,μ}$ implies majorization order $λ\preceqμ$. The conjecture is a close analogy with other known results on Muirhead-type inequalities. In 2021, Heaton and Shankar disproved the conjecture by showing a counterexample for number of variables $n=3$ and degree $d=8$. They then asked whether the conjecture is true when $n$ is sufficiently large. In this paper, we show, by a family of counter-examples, that the conjecture does not hold for any $n$ and any $d$ as long as $n\geq2$ and $d\geq8$. Based on the insights gained from the counter-examples, we propose a new conjecture for the inequality $H_{n,λ}\leq H_{n,μ}$.

math.CO↗
arXiv2024

Enhanced Radiation Hardness of InAs/GaAs Quantum Dot Lasers for Space Communication

Semiconductor lasers have great potential for space laser communication. However, excessive radiation in space can cause laser failure. In principle, quantum dot (QD) lasers are more radiation-resistant than traditional semiconductor lasers because of their superior carrier confinement and smaller active regions. However, the multifaceted nature of radiation effects on QDs resulted in ongoing controversies. Comprehensive testing under simulated space conditions is also necessary to validate their performance. In this work, we conducted radiation tests on various In(Ga)As/GaAs QD and quantum well (QW) materials and devices. Our results revealed that InAs/GaAs QDs with filling factors greater than 50% exhibit greater radiation hardness than those below 50%. Furthermore, most InAs/GaAs QDs showed superior radiation resistance compared to InGaAs/GaAs QW when exposed to low proton fluences of 1E11 and 1E12 cm-2, resulting from radiation-induced defects. The linewidth enhancement factor (LEF) of well-designed QD lasers remains remarkably stable and close to zero, even under proton irradiation at a maximum fluence of 7E13 cm-2, owing to their inherent insensitivity to irradiation-induced defects. These QD lasers demonstrate an exceptional average relative intensity noise (RIN) level of -162 dB/Hz, with only a 1 dB/Hz increase in RIN observed at the highest fluence, indicating outstanding stability. Furthermore, the lasers exhibit remarkable robustness against optical feedback, sustaining stable performance even under a feedback strength as high as -3.1 dB. These results highlight the significant potential of QD lasers for space laser communication applications, where high reliability and resilience to radiation and environmental perturbations are critical.

physics.app-ph↗
arXiv2023

Dynamics of a Leslie-Gower type predator-prey system with herd behavior and constant harvesting in prey

In this paper, the dynamics of a Leslie-Gower type predator-prey system with herd behavior and constant harvesting in prey are investigated. Earlier work has shown that the herd behavior in prey merely induces a supercritical Hopf bifurcation in the classic Leslie-Gower predator-prey system in the absence of harvesting. However, the work in this paper shows that the presence of herd behavior and constant harvesting in prey can give rise to numerous kinds of bifurcation at the non-hyperbolic equilibria in the classic Leslie-Gower predator-prey system such as two saddle-node bifurcations and one Bogdanov-Takens bifurcation of codimension two at the degenerate equilibria and one degenerate Hopf bifurcation of codimension three at the weak focus. Hence, the research results reveal that the herd behavior and constant harvesting in prey have a strong influence on the dynamics and also contribute to promoting the ecological diversity and maintaining the long-term economic benefits.

math.DS↗
arXiv2021

Bifurcations of a predator-prey system with cooperative hunting and Holling III functional response

In this paper, we consider the dynamics of a predator-prey system of Gause type with cooperative hunting among predators and Holling III functional response. The known work numerically shows that the system exhibits saddle-node and Hopf bifurcations except homoclinic bifurcation for some special parameter values. Our results show that there are a weak focus of multiplicity three and a degenerate equilibrium with double zero eigenvalues (i.e., a cusp of codimension two) for general parameter conditions and the system can exhibit various bifurcations as perturbing the bifurcation parameters appropriately, such as the transcritical and the pitchfork bifurcations at the degenerate boundary equilibrium, the saddle-node and the Bogdanov-Takens bifurcations at the degenerate positive equilibrium and the Hopf bifurcation around the weak focus. The comparative study demonstrates that the dynamics are far richer and more complex than that of the system without cooperative hunting among predators. The analysis results reveal that appropriate intensity of cooperative hunting among predators is beneficial for the persistence of predators and the diversity of ecosystem.

math.DS↗
arXiv2019

Thermal Brownian Motion of Skyrmion for True Random Number Generation

The true random number generators (TRNGs) have received extensive attention because of their wide applications in information transmission and encryption. The true random numbers generated by TRNG are typically applied to the encryption algorithm or security protocol of the information security core. Recently, TRNGs have also been employed in emerging stochastic computing paradigm for reducing power consumption. Roughly speaking, TRNG can be divided into circuits-based, e.g., oscillator sampling or directly noise amplifying; and quantum physics-based, e.g., photoelectric effect. The former generally requires a large area and has a large power consumption, whereas the latter is intrinsic random but is more difficult to implement and usually requires additional post-processing circuitry. Very recently, magnetic skyrmion has become a promising candidate for implementing TRNG because of their nanometer size, high stability, and intrinsic thermal Brownian motion dynamics. In this work, we propose a TRNG based on continuous skyrmion thermal Brownian motion in a confined geometry at room temperature. True random bitstream can be easily obtained by periodically detecting the relative position of the skyrmion without the need for additional current pulses. More importantly, we implement a probability-adjustable TRNG, in which a desired ratio of 0 and 1 can be acquired by adding an anisotropy gradient through voltage-controlled magnetic anisotropy (VCMA) effect. The behaviors of the skyrmion-based TRNG are verified by using micromagnetic simulations. The National Institute of Standards and Technology (NIST) test results demonstrate that our proposed random number generator is TRNG with good randomness. Our research provides a new perspective for efficient TRNG realization.

physics.app-ph↗
arXiv2019

A sufficient condition for local nonnegativity

A real polynomial $f$ is called local nonnegative at a point $p$, if it is nonnegative in a neighbourhood of $p$. In this paper, a sufficient condition for determining this property is constructed. Newton's principal part of $f$ (denoted as $f_N$) plays a key role in this process. We proved that if every $F$-face, $(f_N)_F$, of $f_N$ is strictly positive over $(\mathbb{R}\setminus 0)^n$, then $f$ is local nonnegative at the origin $O$.

math.AG↗
arXiv2019

Dynamics of a Prey-predator System with Foraging Facilitation in Predators

The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root isolation technique and complete discrimination system of polynomial to obtain parameter conditions for the exact number of equilibria and their qualitative properties as well as a complete investigation of bifurcations including saddle-node, transcritical, pitchfork, Hopf and Bogdanov-Takens bifurcations. Moreover, numerical simulations are presented to support our theoretical results.

math.DS↗
arXiv2018

Arbitrarily routed mode-division multiplexed photonic circuits for dense integration

Mode-division multiplexing (MDM) is becoming an enabling technique for large-capacity data communications via encoding the information on orthogonal guiding modes. However, the on-chip routing of a multimode waveguide occupies too large chip area due to the constraints on inter-mode cross talk and mode leakage. Very recently, many efforts have been made to shrink the footprint of individual element like bending and crossing, but the devices still occupy >10x10 um2 footprint for three-mode multiplexed signals and the high-speed signal transmission has not been demonstrated yet. In this work, we demonstrate the first MDM circuits based on digitized meta-structures which have extremely compact footprints. The radius for a three-mode bending is only 3.9 μm and the footprint of a crossing is only 8x8um2. The 3x100 Gbit/s mode-multiplexed signals are arbitrarily routed through the circuits consists of many sharp bends and compact crossing with a bit error rate under forward error correction limit. This work is a significant step towards the large-scale and dense integration of MDM photonic integrated circuits.

physics.app-ph↗
arXiv2017

The process of 3D-printed skull models for the anatomy education

Objective The 3D printed medical models can come from virtual digital resources, like CT scanning. Nevertheless, the accuracy of CT scanning technology is limited, which is 1mm. In this situation, the collected data is not exactly the same as the real structure and there might be some errors causing the print to fail. This study presents a common and practical way to process the skull data to make the structures correctly. And then we make a skull model through 3D printing technology, which is useful for medical students to understand the complex structure of skull. Materials and Methods The skull data is collected by the CT scan. To get a corrected medical model, the computer-assisted image processing goes with the combination of five 3D manipulation tools: Mimics, 3ds Max, Geomagic, Mudbox and Meshmixer, to reconstruct the digital model and repair it. Subsequently, we utilize a low-cost desktop 3D printer, Ultimaker2, with polylactide filament (PLA) material to print the model and paint it based on the atlas. Result After the restoration and repairing, we eliminate the errors and repair the model by adding the missing parts of the uploaded data within 6 hours. Then we print it and compare the model with the cadaveric skull from frontal, left, right and anterior views respectively. The printed model can show the same structures and also the details of the skull clearly and is a good alternative of the cadaveric skull.

cs.OH↗
arXiv2015

Microwave band gap and cavity mode in spoof-insulator-spoof waveguide with multiscale structured surface

We propose a multiscale spoof-insulator-spoof (SIS) waveguide by introducing periodic geometry modulation in the wavelength scale to a SIS waveguide made of perfect electric conductor. The MSIS consists of multiple SIS subcells. The dispersion relationship of the fundamental guided mode of the spoof surface plasmon polaritons (SSPPs) is studied analytically within the small gap approximation. It is shown that the multiscale SIS possesses microwave band gap (MBG) due to the Bragg scattering. The "gap maps" in the design parameter space are provided. We demonstrate that the geometry of the subcells can efficiently adjust the effective refraction index of the elementary SIS and therefore further control the width and the position of the MBG. The results are in good agreement with numerical calculations by the finite element method (FEM). For finite-sized MSIS of given geometry in the millimeter scale, FEM calculations show that the first-order symmetric SSPP mode has zero transmission in the MBG within frequency range from 4.29 GHz to 5.1 GHz. A cavity mode is observed inside the gap at 4.58 GHz, which comes from a designer "point defect" in the multiscale SIS waveguide. Furthermore, ultrathin MSIS waveguides are shown to have both symmetric and antisymmetric modes with their own MBGs, respectively. The deep-subwavelength confinement and the great degree to control the propagation of SSPPs in such structures promise potential applications in miniaturized microwave device.

physics.optics↗
arXiv2014

A Successive Resultant Projection for Cylindrical Algebraic Decomposition

This note shows the equivalence of two projection operators which both can be used in cylindrical algebraic decomposition (CAD) . One is known as Brown's Projection (C. W. Brown (2001)); the other was proposed by Lu Yang in his earlier work (L.Yang and S.~H. Xia (2000)) that is sketched as follows: given a polynomial $f$ in $x_1,\,x_2,\,\cdots$, by $f_1$ denote the resultant of $f$ and its partial derivative with respect to $x_1$ (removing the multiple factors), by $f_2$ denote the resultant of $f_1$ and its partial derivative with respect to $x_2$, (removing the multiple factors), $\cdots$, repeat this procedure successively until the last resultant becomes a univariate polynomial. Making use of an identity, the equivalence of these two projection operators is evident.

cs.SC↗
arXiv2012

The expansion of real forms on the simplex and applications

If n points B_1,---,B_n$ in the standard simplex Δ_n are affinely independent, then they can span an (n-1)-simplex denoted by Λ=Con(B_1,---,B_n). Here Λcorresponds to an n*n matrix [Λ] whose columns are B_1,---,B_n. In this paper, we firstly proved that if Λof diameter sufficiently small contains a point $P$, and f(P)>0 (<0) for a form f in R[X], then the coefficients of f([Λ] X) are all positive (negative). Next, as an application of this result, a necessary and sufficient condition for determining the real zeros on Δ_n of a system of homogeneous algebraic equations with integral coefficients is established.

math.AG↗
arXiv2011

An algorithm for determining copositive matrices

In this paper, we present an algorithm of simple exponential growth called COPOMATRIX for determining the copositivity of a real symmetric matrix. The core of this algorithm is a decomposition theorem, which is used to deal with simplicial subdivision of $\hat{T}^{-}=\{y\in Δ_{m}| β^Ty\leq 0\}$ on the standard simplex $Δ_m$, where each component of the vector $β$ is -1, 0 or 1.

math.RA↗
arXiv2010

Successive Difference Substitution Based on Column Stochastic Matrix and Mechanical Decision for Positive Semi-definite Forms

The theory part of this paper is sketched as follows. Based on column stochastic average matrix $T_n$ selected as a basic substitution matrix, the method of advanced successive difference substitution is established. Then, a set of necessary and sufficient conditions for deciding positive semi-definite form on $\R^n_+$ is derived from this method. And furthermore, it is proved that the sequence of SDS sets of a positive definite form is positively terminating. Worked out according to these results, the Maple program TSDS3 not only automatically proves the polynomial inequalities, but also outputs counter examples for the false. Sometimes TSDS3 does not halt, but it is very useful by experimenting on so many examples.

cs.SC↗