Tootfinder

Quantum Gravity: are we there yet?
Shahn Majid
https://arxiv.org/abs/2402.18536 https://arxiv.org/pdf/2402.18536

Quantum Gravity: are we there yet?
The turn of the millennium was a time of optimism about an approach to noncommutative geometry inspired by rich mathematical objects called `quantum groups' and its applications to quantum spacetime. This would model quantum gravity effects as noncommutativity of spacetime coordinates and was arguably going to solve quantum gravity itself. It took a further 20 years from that point to develop a particularly suitable formalism of `quantum Riemannian geometry', but this was largely done and has b…

This https://arxiv.org/abs/2202.12287 has been replaced.
link: https://scholar.google.com/scholar?q=a

Davydov-Yetter cohomology and relative homological algebra
Davydov--Yetter (DY) cohomology classifies infinitesimal deformations of the monoidal structure of tensor functors and tensor categories. In this paper we provide new tools for the computation of the DY cohomology for finite tensor categories and exact functors between them. The key point is to realize DY cohomology as relative Ext groups. In particular, we prove that the infinitesimal deformations of a tensor category $\mathcal{C}$ are classified by the 3-rd self-extension group of the tensor …

This https://arxiv.org/abs/2401.16774 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Contractible subshifts
We introduce the notion of a contractible subshift. This is a strengthening of the notion of strong irreducibility, where we require that the gluings are given by a block map. We show that a subshift is a retract of a full shift if and only if it is a contractible SFT with a fixed point. For virtually polycyclic groups, contractibility implies dense periodic points. We introduce a ``homotopy theory'' framework for working with this notion, and ``contractibility'' is in fact simply an analog of …

This https://arxiv.org/abs/2402.17084 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A point-free version of torsionfree classes and the Goldie torsion theor
Torsion theories are a pinnacle in the theory of abelian categories. They are a generalization of torsion abelian groups and in this generalization one of the most studied is that whose torsionfree class consists of nonsingular modules. To introduce the concept of singular interval we use the symmetric idea of torsion theories, that is the torsion class determines the torsionfree class and vice-versa, thus to introduce nonsingular intervals over an upper-continuous modular complete lattice, (a.…

Quantum Gravity: are we there yet?
Shahn Majid
https://arxiv.org/abs/2402.18536 https://arxiv.org/pdf/2402.18536

Quantum Gravity: are we there yet?
The turn of the millennium was a time of optimism about an approach to noncommutative geometry inspired by rich mathematical objects called `quantum groups' and its applications to quantum spacetime. This would model quantum gravity effects as noncommutativity of spacetime coordinates and was arguably going to solve quantum gravity itself. It took a further 20 years from that point to develop a particularly suitable formalism of `quantum Riemannian geometry', but this was largely done and has b…

This https://arxiv.org/abs/2403.08544 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Comparing jet-shaped point symmetry in cluster cooling flows and supernovae
I point out similarities between point-symmetric X-ray morphologies in cooling flow groups and clusters of galaxies, which are observed to be shaped by jets, and point-symmetric morphologies of eight core-collapse supernova (CCSN) remnants. I use these similarities to strengthen the jittering jet explosion mechanism (JJEM) of CCSNe, which predicts that the last pairs of jets to be launched by the newly born neutron star might shape some CCSN remnants to point-symmetric morphology. The point-sym…

Intersecting subsets in finite permutation groups
CaiHeng Li, Venkata Raghu Tej Pantangi, Shujiao Song, Yilin Xie
https://arxiv.org/abs/2403.17783 https://…

Intersecting subsets in finite permutation groups
A subset (subgroup) $S$ of a transitive permutation group $G\leq Sym(Ω)$ is called an intersecting subset (subgroup, resp.) if the ratio $xy^{-1}$ of any elements $x,y\in S$ fixes some point. A transitive group is said to have the EKR property if the size of each intersecting subset is at most the order of the point stabilizer. A nice result of Meagher-Spiga-Tiep (2016) says that 2-transitive permutation groups have the EKR property. In this paper, we systematically study intersecting subsets …

Capturing the Shape of a Point Set with a Line-Segment
Nathan van Beusekom, Marc van Kreveld, Max van Mulken, Marcel Roeloffzen, Bettina Speckmann, Jules Wulms
https://arxiv.org/abs/2402.12285

Capturing the Shape of a Point Set with a Line-Segment
Detecting location-correlated groups in point sets is an important task in a wide variety of applications areas. In addition to merely detecting such groups, the group's shape carries meaning as well. In this paper, we represent a group's shape using a simple geometric object, a line-segment. Specifically, given a radius $r$, we say a line-segment is shape-representing of a point set $P$ if it is within Hausdorff distance $r$ of each point $p \in P$. We aim to find the shortest such line-segmen…

This https://arxiv.org/abs/2310.15035 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Relative Equilibria of Mechanical Systems with Rotational Symmetry
We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The eigenvalues of the locked inertia tensor descend to shape-space and endow it with the geometric structure of a 3-web with the property that any normal relative equilibrium occurs as a critical point of the potential restricted to a leaf from the web. To demonstra…

A point-free version of torsionfree classes and the Goldie torsion theor
Mauricio Medina-B\'arcenas, Martha Lizbeth Shaid Sandoval-Miranda, \'Angel Zald\'ivar-Corichi
https://arxiv.org/abs/2402.17084

A point-free version of torsionfree classes and the Goldie torsion theor
Torsion theories are a pinnacle in the theory of abelian categories. They are a generalization of torsion abelian groups and in this generalization one of the most studied is that whose torsionfree class consists of nonsingular modules. To introduce the concept of singular interval we use the symmetric idea of torsion theories, that is the torsion class determines the torsionfree class and vice-versa, thus to introduce nonsingular intervals over an upper-continuous modular complete lattice, (a.…

Quantized semisimple Lie groups
Rita Fioresi, Robert Yuncken
https://arxiv.org/abs/2403.17180 https://arxiv.org/pdf/2403.17180…

Quantized semisimple Lie groups
These notes present a quick introduction to the q-deformations of semisimple Lie groups from the point of view of unitary representation theory. In order to remain concrete, we concentrate entirely on the case of the lie algebra $\mathrm{sl}(2,\mathbb{C})$ and its associated compact and complex semisimple Lie groups $\mathrm{SU}(2)$ and $\mathrm{SL}(2,\mathbb{C})$. We treat the following topics: The quantized enveloping algebra and its representations; Hopf algebras and the various notions of…

Classification of electronic nematicity in three-dimensional crystals and quasicrystals
Matthias Hecker, Anant Rastogi, Daniel F. Agterberg, Rafael M. Fernandes
https://arxiv.org/abs/2402.17657

Classification of electronic nematicity in three-dimensional crystals and quasicrystals
Electronic nematic order has been reported in a rich landscape of materials, encompassing not only a range of intertwined correlated and topological phenomena, but also different underlying lattice symmetries. Motivated by these findings, we investigate the behavior of electronic nematicity as the spherical symmetry of three-dimensional (3D) space is systematically lowered by the lattice environment. We consider all 32 crystallographic point groups as well as 4 major classes of quasicrystalline…

This https://arxiv.org/abs/2312.13251 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The 2-rank of finite groups acting on hyperelliptic 3-manifolds
We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to $S^3.$ Such involutions are called \textit{hyperelliptic} as the manifolds admitting such an action. We prove that the sectional 2-rank of a finite group acting on a 3-manifold and containing a hyperelliptic involution with fixed-point set with two components has sectional 2-rank at most four; this upper bound is sharp. The cases where the hyperelliptic involution has a fixed-point set…

This https://arxiv.org/abs/2403.08544 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_…

Comparing jet-shaped point symmetry in cluster cooling flows and supernovae
I point out similarities between point-symmetric X-ray morphologies in cooling flow groups and clusters of galaxies, which are observed to be shaped by jets, and point-symmetric morphologies of eight core-collapse supernova (CCSN) remnants. I use these similarities to strengthen the jittering jet explosion mechanism (JJEM) of CCSNe, which predicts that the last pairs of jets to be launched by the newly born neutron star might shape some CCSN remnants to point-symmetric morphology. The point-sym…

GROS: A General Robust Aggregation Strategy
Alejandro Cholaquidis, Emilien Joly, Leonardo Moreno
https://arxiv.org/abs/2402.15442 https://

GROS: A General Robust Aggregation Strategy
A new, very general, robust procedure for combining estimators in metric spaces is introduced GROS. The method is reminiscent of the well-known median of means, as described in \cite{devroye2016sub}. Initially, the sample is divided into $K$ groups. Subsequently, an estimator is computed for each group. Finally, these $K$ estimators are combined using a robust procedure. We prove that this estimator is sub-Gaussian and we get its break-down point, in the sense of Donoho. The robust procedure in…

2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II
Netan Dogra
https://arxiv.org/abs/2403.07476 https://

2-descent for Bloch--Kato Selmer groups and rational points on hyperelliptic curves II
We give refined methods for proving finiteness of the Chabauty--Coleman--Kim set $X(\mathbb{Q}_2 )_2 $, when $X$ is a hyperelliptic curve with a rational Weierstrass point. The main developments are methods for computing Selmer conditions at $2$ and $\infty$ for the mod 2 Bloch--Kato Selmer group associated to the higher Chow group $\mathrm{CH}^2 (\mathrm{Jac}(X),1)$. As a result we show that most genus 2 curves in the LMFDB of Mordell--Weil rank 2 with exactly one rational Weierstrass point sa…

Revisiting holographic model for thermal and dense QCD with a critical point
Qingxuan Fu, Song He, Li Li, Zhibin Li
https://arxiv.org/abs/2404.12109 https:…

Revisiting holographic model for thermal and dense QCD with a critical point
To quantitatively provide reliable predictions for the hot and dense QCD matter, a holographic model should be adjusted to describe first-principles lattice results available at vanishing baryon chemical potential. The equation of state from two well-known lattice groups, the HotQCD collaboration and the Wuppertal-Budapest (WB) collaboration, shows visible differences at high temperatures. We revisit the Einstein-Maxwell-dilaton (EMD) holographic model for hot QCD with 2+1 flavors and physical …

Generation of multiple bound states in the continuum through doubly degenerate quasi-guided modes
Tetsuyuki Ochiai
https://arxiv.org/abs/2404.16472 https:/…

Generation of multiple bound states in the continuum through doubly degenerate quasi-guided modes
We present a detailed theoretical analysis of a peculiar generation of multiple bound states in the continuum (BICs) in two-dimensional periodic arrays of dielectric spheres. They emerge in high-symmetry lattices with the $C_{6v}$ and $C_{4v}$ point groups and involve doubly degenerate quasi-guided modes at the $Γ$ point that can couple to external radiation. By tuning a system parameter, the doubly degenerate modes can exhibit accidental BICs at a critical parameter. In the vicinity of the cr…

This https://arxiv.org/abs/2303.03175 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Residue maps, Azumaya algebras, and buildings
The goal of this note is to give an explicit formula for the residues of twists of the matrix algebra in terms of the twisting cocycle. Combined with the Fixed Point Theorem for actions of finite groups on affine buildings, this leads to a quick proof of the well-known characterization of unramified algebras in terms of Azumaya algebras.

This https://arxiv.org/abs/2402.11982 has been replaced.
initial toot: https://mastoxiv.page/@a…

Non-magnetic layers with a single Dirac cone at high-symmetry point of the Brillouin zone
It is well known that a single Dirac cone at high-symmetry point (HSP) of a Brillouin zone, akin to the one in graphenes' band structure, can not appear as the only quasiparticle at the Fermi level in two-dimensional (2D), non-magnetic materials. Here we found two layer groups with time-reversal symmetry, among all possible both without- and with spin-orbit coupling, that host one Dirac cone at HSP and we show which additional dispersions appear: a pair of Dirac lines on opposite BZ edges and a…

This https://arxiv.org/abs/2204.10354 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Constructive Proof that Many Groups with Non-Torsion 2-Cohomology are Not Matricially Stable
A discrete group is matricially stable if every function from the group to a complex unitary group that is "almost multiplicative" in the point-operator norm topology is "close" to a genuine unitary representation. It follows from a recent result due to Dadarlat that all amenable, groups with non-torsion integral 2-cohomology are not matricially stable, but the proof does not lead to explicit examples of asymptotic representations that are not perturbable to genuine representations. The purpose…

Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
Hsian-Yang Chen, Ching Hung Lam
https://arxiv.org/abs/2402.13621

Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras
We continue our study of cyclic orbifolds of lattice vertex operator algebras and their full automorphism groups. We consider some special isometry $g\in O(L)$ such that $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$. We show that when $L_2=\emptyset$ and $g^i$ is fixed point free on $L$ for any $1\leq i\leq |g|-1$, $V_L^{\hat{g}}$ has extra automorphisms implies either (1) the order of $g$ is a prime or (2) $L$ is isometric to the Leech lattice or some coinvar…

Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry
Ale\v{s} N\'avrat, Lenka Zalabov\'a
https://arxiv.org/abs/2404.01831

Sub-Riemannian optimal synthesis for Carnot groups with the structure of a path geometry
This paper explicitly constructs the complete set of optimal sub-Riemannian geodesics starting from a point for certain Carnot groups of step two. These are groups of dimension 2n+1 equipped with a left-invariant distribution of dimension n+1 such that at each point, there is a unique direction defining a nontrivial Lie bracket. A suitable explicit expression of geodesics, together with symmetries of the structure, allows us to identify the cut time and the cut locus by applying the so-called e…

"…#platforms realized that an infinite supply of teenage creators are cheaper to deal with than media companies or groups of media individuals or powerful creators.
…#YouTubers [are] retiring or taking a step back. It just feels like eventually you hit a point where there’s nothing left here…

This https://arxiv.org/abs/2312.13251 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The 2-rank of finite groups acting on hyperelliptic 3-manifolds
We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to $S^3.$ Such involutions are called \textit{hyperelliptic} as the manifolds admitting such an action. We prove that the sectional 2-rank of a finite group acting on a 3-manifold and containing a hyperelliptic involution with fixed-point set with two components has sectional 2-rank at most four; this upper bound is sharp. The cases where the hyperelliptic involution has a fixed-point set…

Comparing jet-shaped point symmetry in cluster cooling flows and supernovae
Noam Soker (Technion, Israel)
https://arxiv.org/abs/2403.08544 https://<…

Comparing jet-shaped point symmetry in cluster cooling flows and supernovae
I point out similarities between point-symmetric X-ray morphologies in cooling flow groups and clusters of galaxies, which are observed to be shaped by jets, and point-symmetric morphologies of eight core-collapse supernova (CCSN) remnants. I use these similarities to strengthen the jittering jet explosion mechanism (JJEM) of CCSNe, which predicts that the last pairs of jets to be launched by the newly born neutron star might shape some CCSN remnants to point-symmetric morphology. The point-sym…

This https://arxiv.org/abs/2204.10354 has been replaced.
link: https://scholar.google.com/scholar?q=a

A Constructive Proof that Many Groups with Non-Torsion 2-Cohomology are Not Matricially Stable
A discrete group is matricially stable if every function from the group to a complex unitary group that is "almost multiplicative" in the point-operator norm topology is "close" to a genuine unitary representation. It follows from a recent result due to Dadarlat that all amenable, groups with non-torsion integral 2-cohomology are not matricially stable, but the proof does not lead to explicit examples of asymptotic representations that are not perturbable to genuine representations. The purpose…

Bredon motivic cohomology of the real numbers
Bill Deng, Mircea Voineagu
https://arxiv.org/abs/2404.06697 https://arxiv.org/pdf/2404.…

Bredon motivic cohomology of the real numbers
Over the real numbers with $\Z/2-$coefficients, we compute the $C_2$-equivariant Borel motivic cohomology ring, the Bredon motivic cohomology groups and prove that the Bredon motivic cohomology ring of the real numbers is a proper subring in the $RO(C_2\times C_2)$-graded Bredon cohomology ring of a point. This generalizes Voevodsky's computation of the motivic cohomology ring of the real numbers to the $C_2$-equivariant setting. These computations are extended afterwards to any real closed f…

Comparing jet-shaped point symmetry in cluster cooling flows and supernovae
Noam Soker (Technion, Israel)
https://arxiv.org/abs/2403.08544 https://<…

Comparing jet-shaped point symmetry in cluster cooling flows and supernovae
I point out similarities between point-symmetric X-ray morphologies in cooling flow groups and clusters of galaxies, which are observed to be shaped by jets, and point-symmetric morphologies of eight core-collapse supernova (CCSN) remnants. I use these similarities to strengthen the jittering jet explosion mechanism (JJEM) of CCSNe, which predicts that the last pairs of jets to be launched by the newly born neutron star might shape some CCSN remnants to point-symmetric morphology. The point-sym…

This https://arxiv.org/abs/2402.11982 has been replaced.
initial toot: https://mastoxiv.page/@a…

Non-magnetic layers with a single Dirac cone at high-symmetry point of the Brillouin zone
It is well known that a single Dirac cone at high-symmetry point (HSP) of a Brillouin zone, akin to the one in graphenes' band structure, can not appear as the only quasiparticle at the Fermi level in two-dimensional (2D), non-magnetic materials. Here we found two layer groups with time-reversal symmetry, among all possible both without- and with spin-orbit coupling, that host one Dirac cone at HSP and we show which additional dispersions appear: a pair of Dirac lines on opposite BZ edges and a…

Opinion dynamics of two populations with time-delayed coupling
Chiara Cicolani, Cristina Pignotti
https://arxiv.org/abs/2404.07007 https://

Opinion dynamics of two populations with time-delayed coupling
We study a Hegselmann-Krause type opinion formation model for a system of two populations. The two groups interact with each other via subsets of individuals, namely the leaders, and natural time delay effects are considered. By using careful estimates of the system's trajectories, we are able to prove an asymptotic convergence to consensus result. Some numerical tests illustrate the theoretical result and point out some possible applications.

Toroidal orders and related phenomena in nonmagnetic and magnetic materials
Hiroaki Kusunose, Satoru Hayami
https://arxiv.org/abs/2403.09492 https://

Toroidal orders and related phenomena in nonmagnetic and magnetic materials
In this short article, we overview a concept of electronic toroidal multipoles, and their ordering with associated physical properties in non-magnetic and magnetic materials. The toroidal multipoles are introduced as microscopic electronic variables in view of symmetry and connection to Dirac theory. They are classified according to crystallographic and magnetic point groups, which allows us to discuss various possible cross correlations in a transparent and unified manner. The representative e…

An entropic analisis of social demonstrations
Daniel Rico, Y\'erali Gandica
https://arxiv.org/abs/2404.06965 https://arxiv.org/pd…

An entropic analisis of social demonstrations
Social media has dramatically influenced how individuals and groups express their demands, concerns and aspirations during social demonstrations. The study of X or Twitter hashtags during those events has revealed the presence of some temporal points characterised by high correlation among their participants. It has also been reported that the connectivity presents a modular-to-nested transition at the point of maximum correlation. The present study aims to determine whether it is possible to c…

Dynamics of primitive elements under group actions
Pratyush Mishra
https://arxiv.org/abs/2403.16769 https://arxiv.org/pdf/2403.16769<…

Dynamics of primitive elements under group actions
We investigate group actions in which certain primitive elements fix a point, while not all group elements possess this property when acting upon some space. Using similar dynamical tools, we introduce the notion of Nielsen girth and prove the existence of groups with infinite girth but having finite Nielsen girth.

Homogeneous quandles with abelian inner automorphism groups and vertex-transitive graphs
Konomi Furuki, Hiroshi Tamaru
https://arxiv.org/abs/2403.06209 htt…

Homogeneous quandles with abelian inner automorphism groups and vertex-transitive graphs
A quandle is an algebraic system originated in knot theory, and can be regarded as a generalization of symmetric spaces. The inner automorphism group of a quandle is defined as the group generated by the point symmetries (right multiplications). In this paper, starting from any simple graphs, we construct quandles whose inner automorphism groups are abelian. We also prove that the constructed quandle is homogeneous if and only if the graph is vertex-transitive. This shows that there is a wide f…

Random Groups are not $n$-Cubulated
Zachary Munro
https://arxiv.org/abs/2403.08522 https://arxiv.org/pdf/2403.08522

Random Groups are not $n$-Cubulated
A group $G$ has $F\mathcal C_n$ if every action on a $n$-dimensional $\mathrm{CAT}(0)$ cube complex has a global fixed point. This provides a natural stratification between Serre's $FA$ and Kazhdan's $(T)$. For every $n$, we show that random groups in the plain words density model have $F\mathcal C_n$ with overwhelming probability. The same result holds for random groups in the reduced words density model assuming there are sufficiently many generators. These are the first examples of cubulated…

This https://arxiv.org/abs/2401.17893 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cosmological solutions in the Brans-Dicke theory via invariants of symmetry groups
We proceed to obtain an exact analytical solution of the Brans-Dicke (BD) equations for the spatially flat ($k=0$) Friedmann-Lamaitre-Robertson-Walker (FLRW) cosmological model in both cases of the absence and presence of the cosmological constant. The solution method that we use to solve the field equations of the BD equations is called the "invariants of symmetry groups method" (ISG-method). This method is based on the extended Prelle-Singer (PS) method and it employs the Lie point symmetry, …

Random Groups are not $n$-Cubulated
Zachary Munro
https://arxiv.org/abs/2403.08522 https://arxiv.org/pdf/2403.08522

Random Groups are not $n$-Cubulated
A group $G$ has $F\mathcal C_n$ if every action on a $n$-dimensional $\mathrm{CAT}(0)$ cube complex has a global fixed point. This provides a natural stratification between Serre's $FA$ and Kazhdan's $(T)$. For every $n$, we show that random groups in the plain words density model have $F\mathcal C_n$ with overwhelming probability. The same result holds for random groups in the reduced words density model assuming there are sufficiently many generators. These are the first examples of cubulated…

This https://arxiv.org/abs/1911.06299 has been replaced.
link: https://scholar.google.com/scholar?q=a

Anomalous Hall Effects in Chiral Superconductors
We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E$_1$ and E$_2$ representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and -- as we highlight -- the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the …

This https://arxiv.org/abs/2310.19772 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Exact FLRW cosmological solutions via invariants of the symmetry groups
Until now, various methods have been demonstrated to solve the Friedmann-Lama\'ıtre-Robertson-Walker (FLRW) equations in the spatially flat $(k=0)$ cosmological model. In this study, in order to solve the field equations of the spatially flat FLRW cosmological model in the presence of $Λ$, a new method based on the invariants of the symmetry groups which we called ISG-method, is presented. This method is based on the extended Prelle-Singer (PS) method and it uses the Lie point symmetry, $λ$-…

This https://arxiv.org/abs/2310.19772 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Exact FLRW cosmological solutions via invariants of the symmetry groups
Until now, various methods have been demonstrated to solve the Friedmann-Lama\'ıtre-Robertson-Walker (FLRW) equations in the spatially flat $(k=0)$ cosmological model. In this study, in order to solve the field equations of the spatially flat FLRW cosmological model in the presence of $Λ$, a new method based on the invariants of the symmetry groups which we called ISG-method, is presented. This method is based on the extended Prelle-Singer (PS) method and it uses the Lie point symmetry, $λ$-…