搜索结果：3-in-1

Let $q$ be a power of $2$ and let $\mathbb{F}_q$ be the finite field with $q$ elements. For a positive integer $n$, the polynomial $X^n-1\in\mathbb{F}_q[X]$ is called $3$-sparse over $\mathbb{F}_q$ if every monic irreducible factor of $X^n-1$ over $\mathbb{F}_q$ has at most three nonzero terms. This corrected version gives the characteristic-two classification. Writing $n=2^λm$ with $m$ odd, $X^n-1$ is $3$-sparse over $\mathbb{F}_q$ if and only if either $\rad(m)\mid q^2-1$, or $q=2^e$, $3 mid e$, and $m$ lies in the exceptional $7$-family \[ m=7^A s_0, \quad A\ge1, \quad (s_0,7)=1, \quad \rad(s_0)\mid q-1, \quad 3 mid s_0/\gcd(s_0,q-1), \] with the additional maximal $7$-adic orbit condition $\ord_{7^a}(q)=3\cdot7^{a-1}$ for $1\le a\le A$. The latter condition is equivalent to $A=1$ or $7 mid e$. This condition is necessary; for example, $X^{49}-1$ is not $3$-sparse over $\mathbb{F}_{128}$.

We report a 4.9\,ppb measurement of the positronium $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ interval using continuous-wave two-photon laser spectroscopy. The transition is detected via photoionization by the same excitation laser. The resulting positrons are guided to a microchannel plate detector, surrounded by scintillators to detect the annihilation photons in coincidence, thereby reducing the background. A Monte Carlo lineshape simulation, accounting for effects such as the second-order Doppler shift and the AC Stark shift, is used to extract a transition frequency of $1233607224.1(6.0)\,\text{MHz}$, consistent with the previous 2.6\,ppb determination of this transition and with the most recent QED calculations at order $\mathcal{O}(α^7\ln^2(1/α))$, which predict $1233607222.12(58)\,\text{MHz}$. Combining the two measurements gives $1233607218.1(2.8)\,\text{MHz}$, reducing the tension with QED to about $1.4\,σ$. We also present a semi-analytical lineshape model of $\text{1}^\text{3}\text{S}_\text{1} \to \text{2}^\text{3}\text{S}_\text{1}$ of positronium, which shows excellent agreement with detailed simulations and is validated by the experim

Two main ingredients of current particle physics such as local gauge symmetry and mass generation via the Higgs mechanism being basic ground of the Standard Model are widely confirmed by experimental data. However, some problems such as neutrino masses, dark matter, baryon asymmetry of Universe have clearly indicated that the Standard Model cannot be the ultimate theory of nature. To surpass the mentioned puzzles, many extensions of the Standard Model (called beyond Standard Model) have been proposed. Among beyond Standard Models, the 3-3-1 models have some intriguing features and they get wide attention. The pioneer models develop in some directions. In this paper, %some new main versions of the 3-3-1 models and their consequences are presented.

We investigate a dark photon that arises from the UV model based upon $SU(3)_C\otimes SU(3)_L\otimes U(1)_X \otimes U(1)_G$ (3-3-1-1) gauge symmetry, where the last three factors enlarge the electroweak symmetry encompassing electric charge $Q=T_3 - 1/ \sqrt{3}T_8 +X$ and dark charge $D = -2/\sqrt{3} T_8 +G$. It is well-established that this model addresses the questions of family number, neutrino mass, and dark matter. It is shown in this work that if the 3-3-1-1 breaking scale is much bigger than the dark charge breaking scale, the relevant dark gauge boson $Z'$ is uniquely imprinted at TeV, avoiding dangerous FCNC processes, obeying precision electroweak measurements, as well as contributing to collider phenomena, even if no kinetic mixing is presented. The dark matter observables are perhaps governed by the dark charge breaking Higgs field instead of the dark photon.

Na-ion batteries (NIBs), which are recognized as a next-generation alternative technology for energy storage, still suffer from commercialization constraints due to the lack of low-cost, high-performance cathode materials. Since our first discovery of Cu$^{3+}$/Cu$^{2+}$ electrochemistry in 2014, numerous Cu-substituted/doped materials have been designed for NIBs. However for almost ten years, the potential of Cu$^{3+}$/Cu$^{2+}$ electrochemistry has been grossly underappreciated and normally regarded as a semielectrochemically active redox. Here, we re-synthesized P2-Na$_{2/3}$[Cu$_{1/3}$Mn$_{2/3}$]O$_2$ and reinterpreted it as a high-voltage, cost-efficient, air-stable, long-life, and high-rate cathode material for NIBs, which demonstrates a high operating voltage of 3.7 V and a completely active Cu$^{3+}$/Cu$^{2+}$ redox reaction. The 2.3 Ah cylindrical cells exhibit excellent cycling (93.1% capacity after 2000 cycles), high rate (97.2% capacity at 10C rate), good low-temperature performance (86.6% capacity at -30$^\circ$C), and high safety, based on which, a 56 V-11.5 Ah battery pack for E-bikes is successfully constructed, exhibiting stable cycling (96.5% capacity at the 800th

The smallest possible length of a $q$-ary linear code of covering radius $R$ and codimension (redundancy) $r$ is called the length function and is denoted by $\ell_q(r,R)$. In this work, for $q$ \emph{an arbitrary prime power}, we obtain the following new constructive upper bounds on $\ell_q(3t+1,3)$: $\ell_q(r,3)\lessapprox \sqrt[3]{k}\cdot q^{(r-3)/3}\cdot\sqrt[3]{\ln q},~r=3t+1, ~t\ge1, ~ q\ge\lceil\mathcal{W}(k)\rceil, 18 <k\le20.339,~\mathcal{W}(k)\text{ is a decreasing function of }k ;$ $\ell_q(r,3)\lessapprox \sqrt[3]{18}\cdot q^{(r-3)/3}\cdot\sqrt[3]{\ln q},~r=3t+1,~t\ge1,~ q\text{ large enough}.$ For $t = 1$, we use a one-to-one correspondence between codes of covering radius 3 and codimension 4, and 2-saturating sets in the projective space $\mathrm{PG}(3,q)$. A new construction providing sets of small size is proposed. The codes, obtained by geometrical methods, are taken as the starting ones in the lift-constructions (so-called ``$q^m$-concatenating constructions'') to obtain infinite families of codes with radius 3 and growing codimension $r = 3t + 1$, $t\ge1$. The new bounds are essentially better than the known ones.

In its original version, the minimal 3-3-1 model possess a Landau-pole around 2-6 TeV scale. Current LHC bound on $Z^{\prime}$ implies that the $SU(3)_L\times U(1)_X$ symmetry must break spontaneously around 4 TeV which means that the model may lose its perturbative character even before symmetry breaking. This is a disaster for the model. Few attention has been devoted to this problem. Here we investigate the efficiency of scalar leptoquarks in evading or shifting the Landau pole to a harmless energy scale.

In 3-3-1 models anomaly cancellation requires that one of the three families of quarks transforms as triplet by $\text{SU}(3)_\text{L}$ with the other two transforming necessarily as anti-triplet. This is an important feature of the model because with it we explain family replication. Thus it is mandatory to discriminate which of the families will transform as triplet by $\text{SU}(3)_\text{L}$ because the main consequence of anomaly cancellation in 3-3-1 models is the arising of processes violating flavor at tree level by means of neutral currents mediated by gauge and scalar fields and each case leads to different results. In this work we consider the 3-3-1 model with right-handed neutrinos. Among the spectrum of 3-3-1 particles that contributes to the flavor changing neutral processes, there is a pseudoscalar that may be the lightest of the 3-3-1 particles and then should give the main contribution to such processes. We then calculate its contribution to the $K^0 -\bar K^0$ mixing transition and confront it with the current experimental results. We do this for the three cases in which one of the family of quarks transforms as a triplet by $\text{SU}(3)_\text{L}$. According to ou

Expanding General Relativity in the inverse speed of light, 1/c, leads to a nonrelativistic gravitational theory that extends the Post-Newtonian expansion by the inclusion of additional strong gravitational potentials. This theory has a fully covariant formulation in the language of Newton-Cartan geometry but we revisit it here in a 3+1 formulation. The appropriate 3+1 formulation of General Relativity is one first described by Kol and Smolkin (KS), rather than the better known Arnowitt-Deser-Misner (ADM) formalism. As we review, the KS formulation is dual to the ADM formulation in that the role of tangent and co-tangent spaces get interchanged. In this 3+1 formulation the 1/c expansion can be performed in a more systematic and efficient fashion, something we use to extend the computation of the effective Lagrangian beyond what was previously achieved and to make a number of new all order observations.

Money would keep coal plants open, build the first new plants in over a decade

A lightweight new X-ray telescope could finally give scientists something they’ve never had before: a complete chemical map of the Moon。 Researchers used detailed mission simulations to show that a compact telescope orbiting the Moon could identify key elements across the entire lunar surface, helping reveal how the Moon formed and evolved

Scientists have developed a solar desalination system that turns seawater into drinking water without creating environmentally damaging brine。 Special laser-textured metal panels use sunlight to evaporate water while automatically moving salt deposits away from the working surface, preventing clogging。 The process was successfully tested with water

What’s the difference between a person, an artifact, and an ecosystem

FCC did not violate carriers' right to jury trial, court says in 8-1 ruling

Astronomers have finally cracked the mystery behind a strange class of repeating cosmic signals that has baffled scientists for years。 Using Australia’s ASKAP radio telescope, researchers traced the bursts to a rare stellar duo in which a dense white dwarf is relentlessly siphoning material from a nearby red dwarf companion。 As the stolen matter sp

The Huracan gave us the R8s, now the Temerario lends itself to a new Audi

Scientists have uncovered a surprising new way to control superconductivity — the mysterious phenomenon where electricity flows with zero energy loss。 By pairing twisted layers of graphene with a synthetic diamond material, researchers were able to effectively switch superconductivity on and off by tweaking how electrons interact with their surroun

Scientists working at CERN’s Large Hadron Collider may be seeing the strongest hints yet of physics beyond the Standard Model — the decades-old theory that explains the fundamental particles and forces of the universe。 By studying incredibly rare particle transformations called “penguin decays,” researchers found behavior that doesn’t fully match t

A new AI-powered chip from UC Davis can analyze light and chemicals using a device tiny enough to fit almost anywhere。 By combining smart silicon sensors with machine learning, it achieves lab-style spectral analysis without the bulky equipment