Joonas Ilmavirta · arXiv (Cornell University) · 2014
If $G$ is a finite group, is a function $f:G\to\mathbb C$ determined by its sums over all cosets of cyclic subgroups of $G$? In other words, is the Radon transform on $G$ injective? This inverse problem is a discrete analogue of asking whether a function on a compact Lie group is determined by its integrals over all geodesics. We discuss what makes this new discrete inverse problem analogous to well-studied inverse problems on manifolds and we also present some alternative definitions. We use representation theory to prove that the Radon transform fails to be injective precisely on Frobenius complements. We also give easy-to-check sufficient conditions for injectivity and noninjectivity for the Radon transform, including a complete answer for abelian groups and several examples for nonabelian ones.
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Shanding Xu, Xiwang Cao, Guangkui Xu · IET Communications · 2016
In this study, first the authors present a simplified representation of the Peng–Fan bounds on the periodic Hamming correlation of frequency‐hopping sequence (FHS) sets, which may also be used to check the optimality of an FHS set with respect to the Peng–Fan bounds. Second, they propose a recursive construction of FHS sets from the known ones using some injective functions and the Chinese remainder theorem. It generalises the previous construction of optimal FHSs and FHS sets with composite lengths employing a given function. Without the limit of the specific function, their construction can produce new optimal FHSs and FHS sets that cannot be produced by the earlier construction. By choosing appropriate injective functions and known optimal FHSs and FHS sets, infinitely many new optimal FHSs and FHS sets can be recursively obtained.
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Sudev Naduvath, K. A. Germina · Carpathian Mathematical Publications · 2015
Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-labeling (IASL) of a graph $G$ is an injective set-valued function $f:V(G)\to\mathcal{P}(\mathbb{N}_0)\setminus\{\emptyset\}$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)\setminus \{\emptyset\}$ is defined by $f^+(uv) = f(u)+ f(v)$, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. A graph which has an IASL is usually called an IASL-graph. An IASL $f$ of a graph $G$ is said to be an integer additive set-indexer (IASI) of $G$ if the associated function $f^+$ is also injective. In this paper, we define the notion of integer additive set-labeling of signed graphs and discuss certain properties of signed graphs which admits certain types of integer additive set-labelings.
Cited by 6Open access
S. Lagrange · 2016
Abstract. This paper presents a new numerical algorithm based on interval analysis able to verify that a continuously differentiable function is injective. The efficiency of the method is demonstrated by illustrative examples. These examples have been treated by a C++ solver which is made available.
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Raja Ponraj, Jeyaraj Vijaya, Xavier Parthipan · 2011
Let G be a , p q graph. An injective map : 1, 2,,f V G p is called a pair sum labeling if the induced edge function, :ef E G Z 0 defined by ef uv f u f v is one-one and ef E G
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Sudev, N. K., Germina, K. A. · arXiv (Cornell University) · 2014
Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) of a graph $G$ is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $\mathbb{N}_0$ is the set of all non-negative integers. A graph $G$ which admits an IASI is called an IASI graph. An IASI of a graph $G$ is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of $G$ are in arithmetic progressions. In this paper, we discuss about two special types of arithmetic IASIs.
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Sudev Naduvath, K. A. Germina · arXiv (Cornell University) · 2014
An integer additive set-indexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$. If $g_f(uv)=k~\forall~uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexers. An integer additive set-indexer $f$ is said to be a strong integer additive set-indexer if $|g_f(uv)|=|f(u)|.|f(v)|~\forall ~ uv\in E(G)$. We already have some characteristics of the graphs which admit strong integer additive set-indexers. In this paper, we study the characteristics of certain graph classes, graph operations and graph products that admit strong integer additive set-indexers.
Cited by 1Open access
Pegg Jr, Ed · Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) · 2011
In the function mapping x->f(x), the domain is all x values and the range is all f(x) values.\nIf f(a)=f(b) implies a=b, the function is called injective, or one-to-one.\nIf for any y in the range there is an x in the domain so that f(x)=y, the function is called surjective, or onto.\nIf both conditions are met, the function is called bijective, or one-to-one and onto
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Pump Industry Analyst · 2003
The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative Lévy noise of affine type. For the second moment of the mild solution, a well-posed deterministic space–time variational problem posed on projective and injective tensor product spaces is derived, which subsequently leads to a deterministic equation for the covariance function.
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Oliver Knill · arXiv (Cornell University) · 2012
We prove that the expectation value of the index function i(x) over a probability space of injective function f on any finite simple graph G=(V,E) is equal to the curvature K(x) at the vertex x. This result complements and links Gauss-Bonnet sum K(x) = chi(G) and Poincare-Hopf sum i(x) = chi(G) which both hold for arbitrary finite simple graphs.
Cited by 36Open access
Daniel J. Bernstein · 2008
Abstract. It is well known that, inside any cryptographic protocol, a uniform random function can be safely replaced with a uniform random injective function: as long as the number of function queries is small, the attacker’s success probability does not noticeably increase. This paper presents a quantitatively stronger theorem that handles a larger number of function queries. This quantitative improvement can be viewed as a generalization of the author’s recent improvement in security bounds for Wegman-Carter-Shoup authenticators. 1
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Barnsley M., Igudesman K. · zvestiya of the National Academy of Sciences of Belarus (National Academy of Sciences of Belarus) · 2012
Overlapping iterated function systems generate families of injective mappings from the attractor onto shift-invariant subsets of the code space. In this paper we consider an example of such a family for the uniformly linear systems of iterated functions on the unit segment. © Allerton Press, Inc., 2012.
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Sudev Naduvath, K. A. Germina · arXiv (Cornell University) · 2014
Let $\mathbb{N}_0$ denote the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer is an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$. If $f^+(uv)=k~\forall~uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=\max(|f(u)|,|f(v)|)~\forall ~ uv\in E(G)$. In this paper, we study the admissibility of weak integer additive set-indexer by certain graphs and graph operations.
Cited by 5Open access
Francisco Fontenele, Frederico Xavier · Journal of Differential Geometry · 2010
The Bieberbach estimate, a pivotal result in the classical theory of univalent functions, states that any injective holomorphic function f on the open unit disc D satisfies |f (0)| 4|f (0)|. We generalize the Bieberbach estimate by proving a version of the inequality that applies to all injective smooth conformal immersions f : D R n , n 2. The new estimate involves two correction terms. The first one is geometric, coming from the second fundamental form of the image surface f (D). The second term is of a dynamical nature, and involves certain Riemannian quantities associated to conformal attractors. Our results are partly motivated by a conjecture in the theory of embedded minimal surfaces.
Cited by 6Open access
Martin Goldstern · Mathematical logic quarterly · 1997
Abstract 1. If A is strongly amorphous (i.e., all relations on A are definable), then its power set P(A) is dually Dedekind infinite, i. e., every function from P(A) onto P(A) is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.
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P. Jiménez-Rodríguez, María E. Martínez-Gómez, Gustavo A. Muñoz-Fernández et al. · Mathematics · 2021
In the present work we study the set of multiplicative convex functions. In particular, we focus on the properties of injectiveness and discontinuity. We will show that a non constant multiplicative convex function is at most 2-injective, and construct multiplicative convex functions which are discontinuous at infinitely many points.
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P Sumathi, G. Geetha Ramani · INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH · 2024
Let G be a simple, finite, connected, undirected, non-trivial graph with vertices and edges. be the vertex set and be the edge set of Let where a and is an injective function. If for each edge defined by is a bijective function then the function is called arithmetic sequential graceful labeling. The graph with arithmetic sequential graceful labeling is called arithmetic sequential graceful graph. In this paper, arithmetic sequential graceful labeling for some special graphs were studied.
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B. D. Acharya, S. Ramanujan, K. A. Germina et al. · MyPrints@UOM (Mysore University Library) · 2010
Given any graph G = (V,E) and an arbitrary nonempty ‘ground set’ X, a linear hypergraph set-indexer (LHSI) is a set-valued function f: V (G) → 2X assigning nonempty subsets of X to the vertices of G and satisfying the following conditions: (i) the ordered pair Hf (G) = (X,f(V)), where f(V) = {f(v) : v ∈ V (G)}, is a ‘simple ’ hypergraph, in the sense that f is injective and ∪v∈V (G)f(v) = X, (ii) Hf (G) is a linear hypergraph, in the sense that |f(u) ∩ f(v) | ≤ 1 ∀ u, v ∈ V, (iii) the induced set-valued function f ⊕ : E → 2X defined by f⊕(uv) = f(u)⊕f(v), ∀ uv ∈ E is injective, and (iv) Hf⊕(G) = (X,f⊕(E)), where f⊕(E) = {f⊕(e) : e ∈ E}, is a linear hypergraph. In this paper, we initiate a study of linear hypergraph set-indexers of a graph.
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A. Rajesh Kannan, K. Loganathan, P. Usha et al. · RePEc: Research Papers in Economics
A graph admits flooring function of centroidal meanness property if its injective node assignment Λ is from 1 to 1+q along with bijective link assignment Λ⋆uv=⌊1/3Γu, vΛu2+Γu, v2+Λv2⌋, where Γu, v=Λu+Λv, is from 1 to q. We examined the flooring function of centroidal meanness values of a few duplicates yielded graphs in this context.
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Yazan Abu Salem, C. Franceschi, Gregorio Alberto et al. · Journal of Cartilage & Joint Preservation · 2026
<h2>Abstract</h2><h3>Background</h3> Meniscal tears, whether degenerative or traumatic, are common causes of knee pain. Concerns regarding long-term joint degeneration after arthroscopic partial meniscectomy have increased interest in joint-preserving injective therapies. <h3>Objectives</h3> To systematically review clinical outcomes, imaging findings, and surgical conversion rates following standalone injective treatments for meniscal pathology. <h3>Data sources</h3> A systematic search of PubMed, Embase, and Cochrane Library was performed on August 29, 2025. <h3>Study eligibility criteria, participants, and interventions</h3> English-language clinical studies (2010–2025) evaluating standalone injective therapies for meniscal tears or degeneration were included. Interventions comprised platelet-rich plasma (PRP), corticosteroids, hyaluronic acid (HA), polynucleotides, microfragmented adipose tissue, and autologous conditioned serum. <h3>Study appraisal and synthesis methods</h3> Data extraction and quality assessment were conducted independently. Methodological quality was assessed using the modified Coleman Methodology Score (CMS) and the Cochrane Risk of Bias 2 tool for randomized controlled trials. <h3>Results</h3> Twenty-four studies (2027 patients) met inclusion criteria. Thirteen evaluated PRP, seven corticosteroids, and four other injective therapies. The mean CMS was 46/100, indicating overall moderate-to-low quality. PRP demonstrated consistent improvements in pain and function, with surgery-free survival exceeding 80% at mid-term follow-up and limited MRI evidence of structural improvement. Corticosteroids provided short-term symptom relief without structural benefit. Other injective therapies showed promising early results but were limited by small sample sizes and heterogeneity. Adverse events and surgical conversion rates were low across treatments. <h3>Limitations</h3> Overall methodological quality was moderate-to-low, with heterogeneity in study design and protocols. <h3>Conclusions and implications of key findings</h3> Injective therapies may provide meaningful symptom relief in selected meniscal lesions. PRP shows the most consistent benefit, while other biologic injectives require higher-quality randomized trials to clarify their role. <h3>Systematic review registration number</h3> CRD420251233155.
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