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Ruijun Wu

Publications and source records attributed to Ruijun Wu.

At least 19 recordsLinked to original sources
arXiv2026

A Study of Bluetooth Access Control Based on NFT Soft Pairing

This paper proposes a Non-Fungible Token (NFT) soft pairing framework for Bluetooth service access control. Unlike conventional Bluetooth systems where pairing implicitly grants persistent service access, the proposed approach decouples native Bluetooth pairing from authorization without modifying the underlying protocol stack. The framework introduces a three-layer architecture consisting of a Bluetooth layer for connectivity, a blockchain layer for trusted execution and on-chain state verification, and an application layer where NFT soft pairing defines the authorization logic. In this design, Non-Fungible Bluetooth Tokens (NFBTs) represent user-side access credentials, while Non-Fungible Device Tokens (NFDTs) represent device identities. Their bidirectional on-chain binding forms a revocable and verifiable NFT soft pairing relationship. During access, users prove ownership of valid NFBTs through challenge-response signatures, and devices verify the corresponding on-chain state before granting service access. A prototype implemented with MetaMask and Ethereum demonstrates secure authentication, dynamic revocation, acceptable latency, and gas-efficient credential issuance based on ERC1155.

cs.CR↗
arXiv2026

Stationary periodic solutions for nonlinear Dirac equations with non-coercive nonlinearity II: splitting

We study stationary periodic solutions of nonlinear Dirac equations with Soler-type nonlinearities. By splitting off a circle factor the problem is reduced to dimension two. The nonlinearity degenerates along a Lorentz null cone, causing difficulties for the variational analysis. Using a coercive perturbation we first obtain minimax perturbed solutions. The key new ingredient is a quantitative separation of the lowest positive eigenspace of the reduced Dirac operator from the null cone; together with a uniform resolvent estimate, it yields uniform bounds that allow us to remove the perturbation. This produces nontrivial periodic solutions for temporal frequencies near the corresponding positive spectral threshold, including frequencies above the mass.

math.AP↗
arXiv2026

Qualitative bifurcation diagram for Grad-Shafranov type equations

We study the qualitative behavior of solutions of Grad-Shafranov type equations arising in plasma physics with general differential operators and general nonlinearities. In particular, we extend recent estimates about threshold values for uniqueness, monotonicity and non-existence of the free boundary. The argument is based on a refined spectral analysis for weighted non-local problems together with comparison techniques and level set analysis.

math.AP↗
arXiv2026

Continuity of Weighted Dirac Spectra

For the weighted Dirac eigenvalue problem, we show that the two-sided weighted spectrum depends continuously on the weight under continuous deformations within a uniformly elliptic class. Moreover, for differentiable families of weights we obtain a quantitative Lipschitz estimate for the full spectrum in the arsinh--metric, based on a weighted Hellmann--Feynman variational identity.

math.SP↗
arXiv2026

Sharp spectral estimates for free boundary problems arising in plasma physics

We derive a sharp spectral estimate for a superlinear free boundary problem arising in plasma physics. The semilinear equation is coupled with a constraint, which forces the analysis of a non-local eigenvalue equation. Consequently the corresponding first eigenvalue, say $\sigma_1$, is not a standard one and it is shown that it cannot satisfy a general isoperimetric property of Faber-Krahn type. This motivates a careful analysis of the problem on balls in any dimension $N\geq 2$, where we prove that in fact $\sigma_1$ is always positive. The implications about the uniqueness problem for the Emden equation are also discussed.

math.AP↗
arXiv2026

Stationary periodic solutions to Nonlinear Dirac equations with non-coercive potentials

Motivated by the Soler model, we study a nonlinear Dirac equation with a non-coercive Soler-type nonlinearity. Stationary periodic solutions are obtained via variational methods. This amounts to studying the equation on a three-dimensional torus, where the spectrum of the physical Dirac operator on the torus needs to be clarified. To overcome the failure of coercivity of the potential we use a coercive perturbation. By carefully analyzing the critical levels and the linking structures, uniform estimates for the perturbed critical points are obtained when the frequency is sufficiently close to the mass. This allows us to pass to the zero-perturbation limit and obtain a nontrivial periodic solution.The argument also extends to suitable scalar external fields.

math.AP↗
arXiv2026

Blockchain-Based Spectrum Resource Securitization via Semi-Fungible Token-Lock

As 6G networks evolve, spectrum assets require flexible, dynamic, and efficient utilization, motivating blockchain based spectrum securitization. Existing approaches based on ERC404 style hybrid token models rely on frequent minting and burning during asset transfers, which disrupt token identity continuity and increase on chain overhead. This paper proposes the Semi Fungible Token Lock (SFT Lock) method, a lock/unlock based mechanism that preserves NFT identity and historical traceability while enabling fractional ownership and transferability. By replacing mint/burn operations with deterministic state transitions, SFT Lock ensures consistent lifecycle representation of spectrum assets and significantly reduces on chain operations. Based on this mechanism, a modular smart contract architecture is designed to support spectrum authorization, securitization, and sharing, and a staking mechanism is introduced to enhance asset liquidity. Experimental results on a private Ethereum network demonstrate that, compared with ERC404 style hybrid token models, the proposed method achieves substantial gas savings while maintaining functional correctness and traceability.

cs.IR↗
arXiv2025

The Rabinowitz continuum of subcritical Gelfand problems and free boundary-type equations arising in plasma physics

The qualitative behavior of the Rabinowitz unbounded continuum of subcritical Gelfand problems is well known on balls in any dimension. We don't know of any such sharp and detailed description otherwise, which is our motivation to look for a new approach to the problem. The underlying idea is to describe solutions of Gelfand problems via suitably defined constrained problems of free boundary-type arising in plasma physics and to replace the usual $L^\infty$ norm of the solution with the energy of the plasma. Toward this goal, we first solve a long standing open problem of independent interest about the uniqueness of solutions of Grad-Shafranov type equations. Thus, we exploit these unique solutions to detect a curve containing both minimal and non minimal solutions of the associated Gelfand problem. In other words we come up with a new global parametrization of the Rabinowitz continuum, the monotonicity of the energy along the branch providing a meaningful generalization of the classical pointwise monotonicity property of minimal solutions, suitable to describe non minimal solutions as well. On a ball in any dimension, we come up as expected with a bell-shaped profile of the full branch of solutions of the Gelfand problem.

math.AP↗
arXiv2025

Weighted eigenvalues of Dirac operators: complete continuity and comparison

We give a min-max characterization of the weighted Dirac eigenvalues, and show that the weighted eigenvalues and eigenspaces of Dirac operators are continuous with respect to weak $L^p$ convergence of the inverse weight, for any $p>n$. Moreover, we establish a comparison result for such weighted eigenvalue problems when there are no harmonic spinors.

math.SP↗
arXiv2025

Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer-Yan spikes revisited

We classify the singular limits relative to a free boundary problem arising in plasma physics in dimension $d=2$, under suitable natural integral bounds. It turns out that one of the asymptotic behaviors allowed corresponds to the Dancer-Yan spikes (J. London Math. Soc. ({\bf 78}) 2008, 639--662). Interestingly enough, roughly speaking and unlike the higher dimensional case, it is not true that any solution in the limit is a Dancer-Yan spike. Indeed, the spiking structure is more rich and we succeed in a detailed description of the singular behavior by a careful analysis, from local to global, of the tiny difference between the maximum value of the spikes and their ``vanishing level'' defining the free boundary.

math.AP↗
arXiv2024

Existence of Solutions to a super-Liouville equation with Boundary Conditions

In this paper, we study the existence of solutions to a type of super-Liouville equation on the compact Riemannian surface $M$ with boundary and with its Euler characteristic $\chi(M)<0$. The boundary condition couples a Neumann condition for functions and a chirality boundary condition for spinors. Due to the generality of the equation, we introduce a weighted Dirac operator based on the solution to a related Liouville equation. Then we construct a Nehari manifold according to the spectral decomposition of the weighted Dirac operator, and use minimax theory on this Nehari manifold to show the existence of the non-trivial solutions.

math.AP↗
arXiv2024

Sharp estimates, uniqueness and spikes condensation for superlinear free boundary problems arising in plasma physics

We are concerned with Grad-Shafranov type equations, describing in dimension $N=2$ the equilibrium configurations of a plasma in a Tokamak. We obtain a sharp superlinear generalization of the result of Temam (1977) about the linear case, implying the first general uniqueness result ever for superlinear free boundary problems arising in plasma physics. Previous general uniqueness results of Beresticky-Brezis (1980) were concerned with globally Lipschitz nonlinearities. In dimension $N\geq 3$ the uniqueness result is new but not sharp, motivating the local analysis of a spikes condensation-quantization phenomenon for superlinear and subcritical singularly perturbed Grad-Shafranov type free boundary problems, implying among other things a converse of the results about spikes condensation in Flucher-Wei (1998) and Wei (2001). Interestingly enough, in terms of the "physical" global variables, we come up with a concentration-quantization-compactness result sharing the typical features of critical problems (Yamabe $N\geq 3$, Liouville $N=2$) but in a subcritical setting, the singular behavior being induced by a sort of infinite mass limit, in the same spirit of Brezis-Merle (1991).

math.AP↗
arXiv2023

On the nodal set of solutions to Dirac equations

Motivated by various geometric problems, we study the nodal set of solutions to Dirac equations on manifolds, of general form. We prove that such set has Hausdorff dimension less than or equal to $n-2$, $n$ being the ambient dimension. We extend this result, previously known only in the smooth case or in specific cases, working with locally Lipschitz coefficients. Under some additional, but still quite general, structural assumptions we provide a stratification result for the nodal set, which appears to be new already in the smooth case. This is achieved by exploiting the properties of a suitable Almgren-type frequency function, which is of independent interest.

math.AP↗
arXiv2023

On the global bifurcation diagram of the equation $-Δu=μ|x|^{2α}e^u$ in dimension two

The aim of this note is to present the first qualitative global bifurcation diagram of the equation $-Δu=μ|x|^{2α}e^u$. To this end, we introduce the notion of domains of first/second kind for singular mean field equations and base our approach on a suitable spectral analysis. In particular, we treat also non-radial solutions and non-symmetric domains and show that the shape of the branch of solutions still resembles the well-known one of the model regular radial case on the disk. Some work is devoted also to the asymptotic profile for $μ\to-\infty$.

math.AP↗
arXiv2022

Geometric analysis of the Yang-Mills-Higgs-Dirac model

The harmonic sections of the Kaluza-Klein model can be seen as a variant of harmonic maps with additional gauge symmetry. Geometrically, they are realized as sections of a fiber bundle associated to a principal bundle with a connection. In this paper, we investigate geometric and analytic aspects of a model that combines the Kaluza-Klein model with the Yang-Mills action and a Dirac action for twisted spinors. In dimension two we show that weak solutions of the Euler-Lagrange system are smooth. For a sequence of approximate solutions on surfaces with uniformly bounded energies we obtain compactness modulo bubbles, namely, energy identities and the no-neck property hold.

math-ph↗
arXiv2022

Existence results for a super Toda system

We solve a super Toda system on a closed Riemann surface of genus~$γ>1$ and with some particular spin structures. This generalizes the min-max methods and results for super Liouville equations and gives new existence results for super Toda systems.

math.AP↗
arXiv2021

Min-max solutions for super sinh-Gordon equations on compact surfaces

In the present paper we initiate the variational analysis of a super sinh-Gordon system on compact surfaces, yielding the first example of non-trivial solution of min-max type. The proof is based on a linking argument jointly with a suitably defined Nehari manifold and a careful analysis of Palais-Smale sequences. We complement this study with a multiplicity result exploiting the symmetry of the problem.

math.AP↗