Papers

One-parameter variational inequalities are well developed, whereas their multi-parameter counterparts remain much less understood. We explore two-parameter variational inequalities for averages over tori in $\mathbb{R}^3$. To capture the underlying two-parameter structure, we introduce a local two-parameter $r$-variation norm that combines rectangular increments with variations along the boundary. The resulting variation operator pointwise dominates the corresponding two-parameter local maximal function and, unlike the maximal function, also captures oscillation across the two parameters. We establish sharp $L^p$–$L^q$ bounds for this variation operator up to endpoints. For comparison, we also obtain sharp $L^p$ bounds up to endpoints for the corresponding local one-parameter variation operator, revealing a genuine difference between the one- and two-parameter boundedness regions. The proof combines square function estimates for two-parameter propagators with local smoothing estimates through mixed-norm interpolation.

In this article, we prove the dynamical Mordell-Lang conjecture for product of endomorphisms on curves defined over complex number field. Moreover, we proved that there is some effectively computable on the the common difference of the arithmetic progressions.

We investigate the existence and nonexistence of least energy solutions for a doubly critical Neumann problem with a critical absorption term. We consider a positive function $u$ defined on a smooth bounded domain $\Omega\subset\mathbb{R}^n$ with $n\ge 5$, satisfying $-\Delta u + \lambda u = u^{2^* - 1} -\alpha u^{2^\sharp-1}$ inside $\Omega$, with Neumann boundary condition $\nabla u\cdot \nu = u^{2^\sharp -1}$ on $\partial\Omega$, where $\lambda>0$, $\alpha\ge0$, $2^*=\frac{2n}{n-2}$ is the critical Sobolev exponent and $2^\sharp=\frac{2(n-1)}{n-2}$ denotes the critical trace exponent. The simultaneous presence of the interior and boundary critical exponents together with this critical absorption term creates a new interaction between competing concentration mechanisms. In particular, the absorption term has the same critical trace exponent as the boundary nonlinearity, but with the opposite sign and acting in the interior of $\Omega$. Consequently, it competes with the boundary mean curvature correction at the same asymptotic order in the energy expansion, leading to a sharp threshold phenomenon. Combining several analytic techniques and geometric tools, we prove the existence of a threshold value $\alpha_{0}=\alpha_{0}(\lambda,\Omega)\in(0,+\infty)$ such that the problem admits a least energy solution if $\alpha<\alpha_{0}$, and no least energy solution if $\alpha>\alpha_{0}$. Moreover, the problem also has a least energy solution at $\alpha =\alpha_0$ provided $\alpha_0> C(n)\max_{\partial \Omega} H$, where $C(n)$ is a positive constant depending only on $n$ and $H$ is the mean curvature on $\partial\Omega$.

Robustness of exponential dichotomies against small-delay perturbations presents a fundamental obstacle: the lack of an effective admissible characterization in nonautonomous delay equations. Considerable efforts have been devoted to obtaining such a characterization for differential equations in Banach spaces. However, even unlike ordinary differential equations, the variation of constants formula for delay equations requires extending the phase space to a space of discontinuous functions, and the dependence on the past states leads to another challenge in establishing exponential dichotomy via admissibility, i.e., constructing a suitable admissible pair and then estimating the growth/decay rates along the unstable/stable subspaces via the admissibility property. In this paper, we provide an admissible characterization based on two pairs of Banach spaces that yields explicit dichotomy exponents. Through this characterization and an operator perturbation method, we prove that small-delay perturbations preserve exponential dichotomies.

We present a frequency-domain formulation of Biot's dynamic poroelastic equations with frequency-dependent dissipation (Biot–Allard) for anisotropic, heterogeneous media with memory effects. Two equivalent two-field representations–a displacement-pressure and a velocity-pressure-rate formulation–enable stabilized iterative splitting. While coupling operators generally lack an adjoint or skew-adjoint relationship at finite frequencies, the velocity–pressure-rate representation restores a skew-adjoint structure in the quasi-static limit. We prove continuity of the coupling operators and coercivity of the diagonal blocks, essential for convergence of the L-stabilized splitting scheme. The frequency-domain setting eliminates convolutional memory terms, incorporates attenuation and dispersion via complex-valued parameters, and reduces the time-dependent problem to a family of elliptic boundary-value problems suited for parallel computation and multi-frequency inversion. A conforming Galerkin finite element discretization preserves block structure, and numerical experiments confirm robustness and capture frequency-dependent attenuation. To illustrate discretization independence, we include a large-scale wave simulation using a pseudo-spectral method. This work provides a rigorous and efficient framework for modeling wave phenomena in complex porous media.

Heterogeneous exascale systems are reshaping computational fluid dynamics, yet rewriting mature high-order solvers for accelerators can fragment code bases and weaken reproducibility. We present a single-source OpenMP target modernisation of UCNS3D, a high-order unstructured finite-volume solver for compressible flows. The common CPU/GPU implementation preserves its numerical formulation, Fortran code base, and workflows. Rather than porting isolated kernels, we enable the complete explicit time-advancement path: high-order reconstruction, gradient evaluation, inviscid and viscous fluxes, boundary treatment, halo exchange, and solution update. The implementation uses persistent target data regions, flat run-time arrays, compile-time sizing of temporary storage, explicit local algebra, target-callable routines, and GPU-aware MPI with device-resident buffers. These choices address the irregular stencils, complex data structures, and substantial temporary storage of high-order unstructured CFD. Verification using the compressible Taylor-Green vortex shows CPU and GPU dissipation histories agreeing to machine precision on LUMI and with published reference data. A single-node run on the ARCHER2 GPU platform provides an independent portability check. End-to-end performance is evaluated on fully populated nodes using Taylor-Green vortex, LM1021 sonic-boom, and NASA high-lift CRM benchmarks. Relative to the previous production implementation, the refactored CPU path is 1.27-1.67 times faster, while GPU offload delivers same-node speed-ups of 2.71-4.05 and 84-101 percent strong-scaling efficiency. The results show that standards-based OpenMP provides portable, production-scale acceleration without sacrificing numerical fidelity, CPU performance, or software sustainability.

For every integer $d\geq2$ and every field of characteristic different from $2$, we prove that on the moduli space $\mathcal{M}_d$ of degree-$d$ rational maps, the multiplier spectrum morphism formed from the periodic points of periods one and two is birational to the closure of its image. Consequently, over every algebraically closed field of characteristic different from $2$, it is generically injective, which proves a recent conjecture of Ji and Xie in characteristic zero. The proof uses a fixed-index normal form, a non-archimedean degeneration of two-cycles, and birational reconstruction of an affine fixed-point configuration from pair invariants.

We prove that join-semidistributive shellable lattices are join-extremal. In particular, every semidistributive shellable lattice is extremal. Together with known results, this gives the equivalence between extremality, left modularity, EL-shellability and shellability for semidistributive lattices. This answers open questions of Mühle and Segovia.

Genuine multipartite Bell nonlocality (GMNL) aims at capturing correlations between many distant observers that are globally Bell nonlocal. A commonly used definition for GMNL is based on biseparable models constructed from non-signalling correlations. Here we uncover an effect of superactivation of GMNL in this framework. Specifically, by locally wiring together two copies of a biseparable correlation, i.e. not GMNL, one can obtain another correlation that is GMNL. We show that this is possible for any number of parties, and for quantum-realizable correlations. Finally, we show that superactivation of GMNL is also possible at the single-copy level, via a catalytic protocol involving only local wirings. These results question the operational meaning of this definition of GMNL.

The purpose of this paper is to classify all the Rota-Baxter operators explicitly on Grassmann algebra in dimension four over the reals.

Let $p_j$ be the prime with index $j$. We prove that the ratios $m/n$ for which $p_m+p_n$ is a square are dense in $\mathbb R_{>0}$. The same is true when $|p_m-p_n|$ is a square. In every nonempty open interval, almost every index can be used as a numerator and as a denominator. We also give a quantitative lower bound for the number of possible partners.

In this paper, we study the low Mach number limit for a compressible two-fluid model with algebraic closure in the $d$-dimensional torus with $d \geq 2$. For large and ill-prepared initial data in critical Besov spaces, we prove that, provided that the Mach number is sufficiently small, the rescaled compressible two-fluid flow exists in critical Besov spaces for any finite time not exceeding the lifespan of the incompressible flow. Moreover, the rescaled compressible two-fluid flow converges to the incompressible Navier–Stokes flow as the Mach number tends to zero. The proof is based on a high-middle-low frequency analysis of the densities and velocity field, combined with a filtering technique involving wave operators. The main novelty is the derivation of new a priori estimates for the high-middle frequency part of the solution to the compressible two-fluid model, depending explicitly on time, the frequency parameter and the Mach number. To the best of our knowledge, this is the first work that proves (almost) global convergence for large and ill-prepared initial data in the low Mach number limit for compressible two-fluid model in critical framework.

Let $\mathbb{N}_0=\{0,1,2,\ldots\}$ and let $h\ge2$ be an integer. For a set $A\subseteq\mathbb{N}_0$, write $hA$ for the set of all sums of $h$, not necessarily distinct, elements of $A$. In this paper, we prove that for every $h\ge2$, there is a partition $\mathbb{N}_0=A\sqcup B$ such that $A$ is a minimal asymptotic basis of order $h$ and $B$ is a maximal asymptotic nonbasis of order $h$. This solves an open problem posed by Nathanson in 1974.

In this paper, we attempt to develop a general notion of representation theory for multiplicative Lie algebras. Consequently, we study equivalent, irreducible, and completely reducible representations. We also introduce the notion of the action of a multiplicative Lie algebra on a vector space and show that there is a one-to-one correspondence between the action and the representation. We also studied the extended structure of a multiplicative Lie algebra through a group.

For any integers $x$ and $y$, let $(x,y)$ and $[x,y]$ stand for the greatest common divisor and the least common multiple of $x$ and $y$, respectively. We denote by $|T|$ the number of elements of a finite set $T$. Let $a,b$ and $n$ be positive integers and let $S=\{x_1,...,x_n\}$ be a set of $n$ distinct positive integers. Let $(f((x_i,x_j)))$ (abbreviated by $f(S)$) and $(f([x_i,x_j]))$ (abbreviated by $(f([S]))$) stand for the $n\times n$ matrices whose $(i,j)-$entry is $(f((x_i,x_j)))$ and $(f([x_i,x_j]))$ respectively. In 1989, Beslin and Ligh gave a description of the lower triangular decomposition of $((x_i,x_j))$. In 1992, Bourque and Ligh showed that if $S$ is factor closed (i.e., S contains all positive divisors of any element of S), then the GCD matrix $((x_i,x_j))$ divides the LCM matrix $([x_i,x_j])$ (written as $((x_i,x_j))|([x_i,x_j])$) in the ring $M_n(\mathbb{Z})$ of $n\times n$ matrices over the integers. In this paper, we will show the diagonalization of $((x_i,x_j))$ and its applications. Our main new contributions are Theorems 4.1 and 4.2, which extend previous results to gcd-closed sets satisfying condition $\mathcal{G}$.

We establish existence, uniqueness, stability, and convergence results for one-dimensional $q$-Bass martingales, characterized as the martingales with prescribed initial and terminal marginals whose transition kernels are closest to a reference measure $q$. Their existence is equivalent to the solvability of a fixed-point problem for probability distributions. Building on Acciaio and Marini (2026), that requires the first marginal to be supported on finitely many points, we study the case of general marginals in convex order. Under the assumption that $q\ll\lambda$, we prove existence, uniqueness and stability of fixed-point distributions, $\mathcal{W}_\infty$-convergence of the fixed-point iteration, and support-diameter estimates. We also extend the martingale Benamou-Brenier formula from Brownian motion to any additive reference process $X$ and show that the corresponding $X$-Bass martingale is optimal whenever it exists, with an interpretation as an adapted Wasserstein projection of $X$.

In Isabelle/HOL, we apply the deep-and-shallow embedding methodology of our prior work to monadic second-order logic (MSO). Three embeddings are developed side by side: a deep embedding (an inductive datatype with an explicit satisfaction relation); a maximal-shallow embedding that translates the connectives and quantifiers directly into HOL, carrying the interpretation and both assignments explicitly; and a minimal-shallow embedding – a locale that fixes those parameters, collapsing the formula type to bool. The enabling new ingredient is a two-sorted substitution apparatus – capture-avoiding substitution, renaming, and a substitution lemma per namespace – in which each binder is transparent for the other; faithfulness of all three embeddings is mechanised and largely automated. Our central contribution is a fully mechanised two-sorted downward Loewenheim-Skolem theorem: the minimal embedding recovers deep validity relative to the (countable) assignment ranges, and this range-relative reading is shown to coincide with the general (Henkin-style) reading of MSO, whereas the standard reading validates strictly more formulas, witnessed by comprehension. Both readings are nonetheless recovered from the minimal embedding, differing only in the admitted interpretations: all of them for the general reading, only the elementary substructures of the full model for the standard. We exercise the embeddings on classical MSO landmarks: the Boolean-closure and graph schemata hold under the full second-order domain yet fail in the minimal embedding, making the dichotomy concrete, while reachability and 2-colorability are refuted throughout.

It is well known that the polymorphism clone of a quasiorder is determined by its unary part, in the sense that any operation is a polymorphism if it satisfies the condition that all unary functions obtained by fixing some of its variables at constant values are polymorphisms. We show that a clone satisfies an analogous property for a particular fixed arity $d$ if and only if it is determined by a collection of what we call higher-dimensional generalized quasiorders whose dimension is equal to $d$. We define higher-dimensional generalized quasiorders with the appropriate generalizations of reflexivity and transitivity to the higher-dimensional setting, which rely on an explicit analysis of 'rectangular' arity.

We develop a set-theoretic translation of a normal modal extension $T_m$ of a recursively axiomatizable first-order theory $T$. We first pass to the Henkin expansion of the underlying language by adding witness constants and work with the sentence algebra of this expansion. The translation is constructed using the corresponding Lindenbaum-Tarski algebra, the Stone space of its ultrafilters, and quotient forcing by a $\sigma$-ideal of Borel sets; in particular, the meager ideal yields Cohen forcing and the null ideal yields the random forcing. In a Boolean-valued universe, we interpret the modal operator $\Box$ by membership of the Boolean value of the translated formula in a suitable filter name. We prove that this translation is sound and complete: a modal formula is provable in $T_m$ if and only if its set-theoretic translation is forced in every associated interpretation. We then build Kripke frames and models from generic extensions and show that the forcing interpretation of $\Box$ agrees with quantification over the corresponding accessibility relation. As a consequence, we obtain completeness with respect to the resulting Kripke models.

In computational fluid dynamics, the numerical simulation of free-surface flows using interface capturing approaches (level set, pseudo-concentration) requires accurate resolution of a transport equation. In the present work, this equation is solved using a new formulation of the Lesaint–Raviart discontinuous Galerkin method, which is particularly suitable for problems without inflow boundaries. The motion is described by the incompressible Navier–Stokes equations with surface tension, discretized using the standard $P2-P1$ Taylor–Hood finite element method in space. Surface tension effects are represented using the so-called Continuum Surface Force model. Finally, the proposed approach is implemented and tested on several benchmarks, including the single rising bubble and the Rayleigh–Taylor instability.

We study seven Eulerian-type polynomial families. We prove that the descent polynomials of derangements are real-rooted, settling the derangement part of a conjecture of S.~Fu, Z.~Lin, and J.~Zeng. We also resolve the real-rootedness conjecture in OEIS A335340, strengthen the known rowwise real-rootedness of an even-top descent family to consecutive strict interlacing, and prove real-rootedness, consecutive interlacing, and real-rooted gamma-polynomials for U.~Shankar's super-Eulerian polynomials. A differential recurrence gives consecutive weak interlacing for ternary words counted by increasing runs. We prove stability of the peak-value refinement and consecutive interleaving of its positive weighted diagonals, settling a conjecture of P.~Alexandersson and O.~Nabawanda. Finally, we prove that the zig-zag Eulerian polynomials, which enumerate swaps in alternating permutations, have simple negative roots, settling the real-rootedness conjecture of T.~Kyle Petersen and Y.~Zhuang.

We consider large time asymptotics of solutions to the damped Schrödinger equation with the nonlinear dissipation in the mass-subcritical case. We prove that the optimal $L^2$-decay rate of the nonlinear solution coincides with that of the corresponding linear solution even in the presence of nonlinear dissipation. Moreover, we give the optimal convergence rate for scattering for any power in the mass-subcritical regime.

For a symmetric weight $w(x)$ on a finite discrete lattice and its Christoffel transforms $x^{2}w(x),x^{2}(x^{2}w(x)),\dots$, we prove that, at each Christoffel step, the conjugated projection associated with the transformed Christoffel–Darboux kernel differs from the original orthogonal projection by a rank-one operator on the subspace of functions vanishing at the origin. This provides a general mechanism for transferring local asymptotic results from an orthogonal polynomial ensemble to its Christoffel-transformed counterpart as the lattice size tends to infinity. As a main application, we study local fluctuations of random Young diagrams arising from skew $(\mathrm{Sp}_{2n},\mathrm{Sp}_{2k})$ Howe duality. The corresponding particle ensemble is obtained from the Krawtchouk orthogonal polynomial ensemble on a quadratic lattice by a Christoffel transform. We identify four asymptotic regimes of local fluctuations in the limit $n,k\to\infty$ with $n/k\to c\in(0,\infty)$. Besides the universal bulk fluctuations governed by the discrete sine kernel and universal Airy fluctuations at the right edge of the limit shape, we obtain the discrete Hermite kernel in the critical regime $(k-n)/\sqrt{n+k}\longrightarrow r\in\mathbb{R}$, and the discrete hard-wall sine kernel at the left corner.

The Julia set is defined by the closure of repelling periodic points in chaotic systems. Why does this structure not appear in integrable systems? In this paper, we address this question by demonstrating the existence of the closure of divergences of the periodic equations, which we designate as the "anti-Julia set." We also call the sets before taking the closures the pre-Julia and pre-anti-Julia sets, respectively. We illustrate the transition mechanism by considering a complex map that interpolates between integrable and non-integrable dynamics, by introducing a real deformation parameter $a$. For $0<a\le 1/2$, we show that the Julia set and the anti-Julia set coincide in the complex plane, although the pre-Julia and pre-anti-Julia sets remain completely disjoint. At the integrable limit $a\to 0$, these two dual structures undergo a critical collision and subsequent annihilation, reminiscent of a cosmological Big Crunch. When $1/2<a<1$, on the other hand, the boundary of the pre-anti-Julia set includes the Julia set. We analytically characterize these phenomena, focusing in particular on the asymptotic behavior of the pre-anti-Julia set as it approaches the integrable limit, and provide numerical visualizations that elucidate the underlying mechanisms of this Big Crunch phenomenon.

The independent set polytope, or stable set polytope, of a graph $G$ is the 0/1-polytope defined by the convex hull of the characteristic vectors of all independent sets of $G$. We present a simple algorithm for computing a Hamilton path on the independent set polytope of a given $n$-vertex graph $G$ with amortized delay $\mathcal{O}(n)$. The independent sets are listed such that two consecutive sets differ either in removing a vertex, or adding a vertex and removing its neighbors from the independent set, i.e., the symmetric difference between two consecutive independent sets induces a star in $G$. As applications of this result, we obtain an algorithm to compute a Hamilton path on the matching polytope of an $m$-edge graph $G$ with worst-case delay $\mathcal{O}(m)$, which lists all matchings of $G$ in such a way that the symmetric difference between two consecutive matchings is a path on at most three edges. Furthermore, we obtain an algorithm to compute a Hamilton path on the chain polytope and order polytope of an $n$-element poset $P$ with amortized delay $\mathcal{O}(n)$, which lists all antichains of $P$ or all ideals of $P$, respectively, by star exchanges. Our algorithms are derived from the generic framework proposed by Merino and Mütze (FOCS'23+SICOMP'24) for computing Hamilton paths on arbitrary 0/1-polytopes, which uses a linear optimization procedure as a black box. Our algorithms bypass solving the computationally intractable maximum weight independent set problem by a simple and purely combinatorial greedy rule.

We develop a two-step procedure for estimating integrated volatility functionals, defined through the occupation measure of the latent spot volatility process, when the asset price is a pure-jump semimartingale. In the first step, block-based estimators formed from absolute powers of high-frequency increments uniformly approximate local averages of powers of volatility. In the second step, these estimates are aggregated into an empirical occupation measure. Since price increments have infinite variance in this setting, arguments based on local Gaussianity are unavailable, and the uniform theory instead rests on maximal inequalities tailored to the stable regime. We establish Glivenko–Cantelli-type uniform consistency over classes of bounded monotone, Lipschitz-in-parameter, and locally Hölder test functions. These results deliver consistent estimation of volatility occupation times and quantiles, together with an argmax-consistency theory for $M$-estimators built on nonparametrically recovered latent processes. We further propose a stability-based rule for selecting the power index of the volatility estimator, which tracks an infeasible ex ante optimal choice closely in Monte Carlo experiments. An application to high-frequency cryptocurrency markets illustrates the framework in a jump-dominated, heavy-tailed environment.

Data-driven constitutive models for path-dependent plasticity are commonly formulated using nonlinear recurrent neural networks, whose sequential state evolution limits parallel training and whose predictions may depend on the discretization of the applied strain path. We introduce a Constitutive State Space (CSS) model that reformulates structured state-space dynamics as an incremental constitutive operator. The strain increment is decomposed into magnitude and direction: the loading direction drives the latent state-space system, while the increment magnitude enters the zero-order-hold discretization of its continuous-time linear recurrence. This mechanics-tailored construction guarantees stationarity under zero increments, strongly reduces sensitivity to strain-path resolution, and retains the parallel-scan structure of S5 for efficient training on long constitutive histories. The CSS and Minimal State Cell (MSC) architectures are compared for four multiaxial path-dependent material models including isotropic J2 plasticity, pressure-sensitive foam plasticity, and combined isotropic-kinematic hardening. CSS matches or exceeds the prediction accuracy of the MSC, including one order of magnitude lower validation losses for the plastically incompressible materials. Importantly, CSS maintains low errors across large changes in strain-path discretization, whereas the MSC error increases substantially when evaluated at coarser resolutions than used for training. CSS trains substantially faster and requires fewer strain-stress pairs to attain comparable or better accuracy. Analysis of the learned state further reveals latent structure consistent with the dimensionality of the underlying physical constitutive models. These results establish mechanics-tailored structured state-space dynamics as a computational framework for efficient and discretization-robust data-driven constitutive modeling.

City logistics addresses the design and management of efficient freight transportation in urban areas. Two-tier networks, where goods are moved by different vehicle fleets from distribution centers to customers using intermediate consolidation facilities, are particularly effective. Although studied from routing, location, and network design perspectives, the research progress is slowed by the lack of standardized, state-of-the-art benchmark data. Many studies rely on outdated and artificial or case-specific instances, limiting reproducibility, comparability, and generality of results. To address this gap, we identify general problem characteristics for two-tier city logistics, provide an instance generation framework CLInstGen that is applicable to a wide range of problem settings, and propose the first benchmark library CLLIB. The library and the CLInstGen code are open-source, allowing researchers to easily use, adapt, and generate instances for their specific applications. CLLIB is based on real-world geographies of urban regions and provides a curated collection of standardized instances for direct benchmarking of models and methods as well as statistical evaluation. A computational study with two different problem settings, namely tactical service network design on two tiers and vehicle routing with simultaneous pickups and deliveries on a single tier, confirms the versatility of both the generator and the library, and provides first numerical and managerial insights on the CLLIB benchmark instances.

The Ramsey number $r(H)$ of a graph $H$ is the minimum positive integer $N$ such that every red/blue edge-coloring of the complete graph $K_N$ on $N$ vertices contains a monochromatic copy of $H$. The Ramsey multiplicity $M(H,n)$ is the minimum number of monochromatic copies of $H$ over all red/blue edge-colorings of $K_n$. It is called threshold Ramsey multiplicity if $n=r(H)$, and denoted by $m(H)$. The only previously known general infinite family for which $m(H)$ has been determined is stars, due to Harary and Prins (1974). Let $C_k$ denote a cycle on $k$ vertices. Conlon, Fox, Sudakov, and Wei (2022) conjectured that $m(C_k)=(k-1)!/2$ for every sufficiently large odd integer $k$. In this paper, we determine $M(C_k,r(C_k)+\ell)$ for every fixed nonnegative integer $\ell$ and all sufficiently large odd $k$, and characterize all extremal colorings, thereby confirming the conjecture. This is also a second general infinite family for which $m(H)$ has been determined.

This paper addresses the problem of semi-global exact prescribed-time stabilization of linear systems by bounded controls. To solve such a problem, one needs to construct a parameterized quadratic control Lyapunov function whose corresponding level set can be made arbitrarily large (for achieving semi-global stabilization) and such that the real parts of the poles of the closed-loop system approach minus infinity as the parameter approaches infinity (for achieving prescribed-time stabilization). This objective is achieved by proposing a nested parametric Lyapunov equation (PLE)-based approach, through which only two linear matrix equations need to be solved in the controller design stage without using real-time state information. Under the proposed structural condition, the nested PLE-based approach guarantees semi-global exact prescribed-time stabilization for any prescribed bounded set of initial conditions, provided that the prescribed settling time is sufficiently large. A numerical example is provided to demonstrate the effectiveness of the designed controller.