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Ahoy, DECmate II the little PDP-8 that could
Now, that's a lot of word processing. But under the hood it's still at least PDP-8 adjacent, even considering its oddities and incompatibilities, and you can make it do many of the things a full-size Eight can. We'll take this basic unit, convert the floppy drives to solid state, tap the video output, and put it through its paces.
One-Shot Klein Cutting Planes for Lipschitz Geodesically Convex Optimization in Hyperbolic Space
arXiv:2605.17540v4 Announce Type: replace Abstract: Motivated by the COLT 2023 open problem of Criscitiello, Mart\'inez-Rubio, and Boumal on deterministic first-order methods for Lipschitz geodesically convex optimization on Hadamard manifolds, we study hyperbolic space \[ \HH^d_{-\kappaC^2} =\{X\in\R^{d+1}:\ipL{X}{X}=-1,\ X_0>0\}, \qquad \ip{U}{V}_X=\kappaC^{-2}\ipL{U}{V}. For every geodesically convex $M$-Lipschitz function \[ f:\bar B_{\HH}(x_0,r)\to\R,\qquad s=\kappaC r, \] we give a...
Approximation by short exponential sums with geometric error decay based on Gauss quadrature
Announce Type: new Abstract: We present new short exponential sum approximations of length $N$ for $f_1(x)=\frac{1}{a+x}$ with $a>0$ on $[0, \infty)$ and for $f_2(x)= {\mathrm e}^{-x^2/2\sigma}$ with $\sigma>0$ on ${\mathbb R}$ with geometric error decay ${\rho}^{-2N}$ for user-defined $N \ge 2$ and $\rho > The approximations are built over consecutive intervals $[b_j, \, b_{j+1}) \subset [0, \infty)$, $j \in {\mathbb N}_{0}$, with interval lengths that depend on $\rho$ and grow...
V-Doped Niobate Nanosheets for Enhanced Photocatalytic Activity
Announce Type: cross Abstract: V-doped [Ca$_{2}$Nb$_{3-x}$V$_{x}$O$_{10}$]$^{-}$ (x = 0, 0.15, 0.3, 0.6, 0.75) nanosheets were produced by solid state reaction followed by protonation and exfoliation by tetrabutylammonium ions. 2D nanosheets have improved photocatalytic activity due to their small thickness that reduces electron-hole recombination, larger surface area that increases photocatalytic sites, and decreased band gap from added V. V-doping has caused the wide band gap of 3.54 eV of...
Generating 2-Gray codes for grand Motzkin paths and grand Dyck paths with air pockets in constant amortized time
Announce Type: cross Abstract: A grand Motzkin path with air pockets is a non-empty lattice path in the first and fourth quadrant of $\mathbb{Z}^2$, starting at the origin $(0,0)$, ending on the $x$-axis, and consisting of up-steps $(1, 1)$, horizontal steps $(1, 0)$, down-steps $(1, -k)$ where $k \geq 1$, and with no consecutive down-steps. A {grand Dyck path with air pockets} is a grand Motzkin path with air pockets that uses no horizontal steps. We present the first known 2-Gray codes for...
Cloning a Sennheiser BA2015 battery pack
One of the annoying things about electronics is that so many companies must make their own incompatible battery packs. For many products these are expensive but at some level still reasonable, the battery pack contains the protection circuitry and some guaranteed high quality Li-ion cells. This is not one of those devices.
Chemical tuning of magnetic ordering and cryogenic magnetocaloric response in zircon-type Gd1-xErxVO4
arXiv:2606.08916v1 Announce Type: cross Abstract: Chemical substitution offers an effective route to tune magnetic ordering and magnetocaloric performance in rare-earth oxides for cryogenic refrigeration. Here we investigate the structural evo lution, magnetic properties, and magnetocaloric effect of polycrystalline zircon-type Gd1-xErxVO4 (x=0, 0.1, 0.25, 0.5, and 0.75). Powder X-ray diffraction confirms that all samples crystallize in the tetragonal zircon structure without detectable...
A Kronecker algorithm for locally closed sets over a perfect field
arXiv:2512.14888v2 Announce Type: replace-cross Abstract: We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety $V$ defined over a perfect field $k$. The variety $V$ is the Zariski closure of the set of common zeros $\{F_1=0,\ldots,F_r=0,G\not=0\}$ of multivariate polynomials $F_1,\ldots,F_r\in k[X_1,\ldots,X_n]$ outside a prescribed hypersurface $\{G=0\}$. We assume that $F_1,\ldots,F_r$...
Exact output statistics of Icart's encoding in the exceptional \(j=0\) case
Announce Type: cross Abstract: Icart's encoding is a classical deterministic map from finite fields to elliptic curves and a basic ingredient in early hash-to-curve constructions. We determine the exact one-output distribution of this map in the exceptional \(j=0\) case. More precisely, for \[ E_{0,b}:Y^2=X^3+b,\ q\equiv2\pmod3, \] we compute the complete fibre distribution of \(f_{0,b}:\mathbb F_q\to E_{0,b}(\mathbb F_q)\).
An Optimal Algorithm for Binary Closest String
arXiv:2605.31417v1 Announce Type: new Abstract: We revisit the Binary Closest String problem, which asks, given a set of binary strings $X \subseteq \{0, 1\}^n$, to compute a string minimizing the maximum Hamming distance to $X$. A long line of work has focused on parameterized algorithms with respect to the optimal distance $d$, yielding a sequence of improvements from $O^*(d^d)$ through $O^*(16^d)$, $O^*(9.513^d)$, $O^*(8^d)$, $O^*(6.731^d)$ to the current best-known running time of...