Thematische Bibliographien / Partial Metric Spaces

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Auswahl der wissenschaftlichen Literatur zum Thema „Partial Metric Spaces“

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Veröffentlicht am 18. Mai 2024

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Zeitschriftenartikel zum Thema "Partial Metric Spaces"

Bukatin, Michael, Ralph Kopperman, Steve Matthews und Homeira Pajoohesh. „Partial Metric Spaces“. American Mathematical Monthly 116, Nr. 8 (01.10.2009): 708–18. http://dx.doi.org/10.4169/193009709x460831.

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Hussain, Nawab, Jamal Rezaei Roshan, Vahid Parvaneh und Abdul Latif. „A Unification ofG-Metric, Partial Metric, andb-Metric Spaces“. Abstract and Applied Analysis 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/180698.

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Using the concepts ofG-metric, partial metric, andb-metric spaces, we define a new concept of generalized partialb-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.

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Aygün, Halis, Elif Güner, Juan-José Miñana und Oscar Valero. „Fuzzy Partial Metric Spaces and Fixed Point Theorems“. Mathematics 10, Nr. 17 (28.08.2022): 3092. http://dx.doi.org/10.3390/math10173092.

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Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown.

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Gregori, Valentín, Juan-José Miñana und David Miravet. „Fuzzy partial metric spaces“. International Journal of General Systems 48, Nr. 3 (Dezember 2018): 260–79. http://dx.doi.org/10.1080/03081079.2018.1552687.

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Oltra, S., S. Romaguera und E. A. Sánchez-Pérez. „Bicompleting weightable quasi-metric spaces and partial metric spaces“. Rendiconti del Circolo Matematico di Palermo 51, Nr. 1 (Februar 2002): 151–62. http://dx.doi.org/10.1007/bf02871458.

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Wu, Yaoqiang. „On weak partial-quasi k-metric spaces“. Journal of Intelligent & Fuzzy Systems 40, Nr. 6 (21.06.2021): 11567–75. http://dx.doi.org/10.3233/jifs-202768.

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In this paper, we introduce the concept of weak partial-quasi k-metrics, which generalizes both k-metric and weak metric. Also, we present some examples to support our results. Furthermore, we obtain some fixed point theorems in weak partial-quasi k-metric spaces.

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Mykhaylyuk, Volodymyr, und Vadym Myronyk. „Metrizability of partial metric spaces“. Topology and its Applications 308 (März 2022): 107949. http://dx.doi.org/10.1016/j.topol.2021.107949.

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Mukheimer, Aiman. „Extended Partial Sb-Metric Spaces“. Axioms 7, Nr. 4 (21.11.2018): 87. http://dx.doi.org/10.3390/axioms7040087.

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In this paper, we introduce the concept of extended partial S b -metric spaces, which is a generalization of the extended S b -metric spaces. Basically, in the triangle inequality, we add a control function with some very interesting properties. These new metric spaces generalize many results in the literature. Moreover, we prove some fixed point theorems under some different contractions, and some examples are given to illustrate our results.

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Yue, Yueli, und Meiqi Gu. „Fuzzy partial (pseudo-)metric spaces“. Journal of Intelligent & Fuzzy Systems 27, Nr. 3 (2014): 1153–59. http://dx.doi.org/10.3233/ifs-131078.

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Ge, Xun, und Shou Lin. „Completions of partial metric spaces“. Topology and its Applications 182 (März 2015): 16–23. http://dx.doi.org/10.1016/j.topol.2014.12.013.

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Dissertationen zum Thema "Partial Metric Spaces"

Putwain, Rosemary Johanna. „Partial translation algebras for certain discrete metric spaces“. Thesis, University of Southampton, 2010. https://eprints.soton.ac.uk/170227/.

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The notion of a partial translation algebra was introduced by Brodzki, Niblo and Wright in [11] to provide an analogue of the reduced group C*-algebra for metric spaces. Such an algebra is constructed from a partial translation structure, a structure which any bounded geometry uniformly discrete metric space admits; we prove that these structures restrict to subspaces and are preserved by uniform bijections, leading to a new proof of an existing theorem. We examine a number of examples of partial translation structures and the algebras they give rise to in detail, in particular studying cases where two different algebras may be associated with the same metric space. We introduce the notion of a map between partial translation structures and use this to describe when a map of metric spaces gives rise to a homomorphism of related partial translation algebras. Using this homomorphism, we construct a C*-algebra extension for subspaces of groups, which we employ to compute K-theory for the algebra arising from a particular subspace of the integers. We also examine a way to form a groupoid from a partial translation structure, and prove that in the case of a discrete group the associated C*-algebra is the same as the reduced group C*-algebra. In addition to this we present several subsidiary results relating to partial translations and cotranslations and the operators these give rise to.

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Sarkar, Koushik. „Topology of different metric spaces and fixed point theories“. Thesis, University of North Bengal, 2021. http://ir.nbu.ac.in/handle/123456789/4380.

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Sarkar, Koushik. „Topology of different metric spaces and fixed point theories“. Thesis, University of North Bengal, 2021. http://ir.nbu.ac.in/handle/123456789/4235.

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O'Neill, Simon John. „A fundamental study into the theory and application of the partial metric spaces“. Thesis, University of Warwick, 1998. http://wrap.warwick.ac.uk/73518/.

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Our aim is to establish the partial metric spaces within the context of Theoretical Computer Science. We present a thesis in which the big "idea" is to develop a more (classically) analytic approach to problems in Computer Science. The partial metric spaces are the means by which we discuss our ideas. We build directly on the initial work of Matthews and Wadge in this area. Wadge introduced the notion of healthy programs corresponding to complete elements in a semantic domain, and of size being the extent to which a point is complete. To extend these concepts to a wider context, Matthews placed this work in a generalised metric framework. The resulting partial metric axioms are the starting point for our own research. In an original presentation, we show that Ta-metrics are either quasi-metrics, if we discard symmetry, or partial metrics, if we allow non-zero self-distances. These self-distances are how we capture Wadge's notion of size (or weight) in an abstract setting, and Edalat's computational models of metric spaces are examples of partial metric spaces. Our contributions to the theory of partial metric spaces include abstracting their essential topological characteristics to develop the hierarchical spaces, investigating their To-topological properties, and developing metric notions such as completions. We identify a quantitative domain to be a continuous domain with a To-metric inducing the Scott topology, and introduce the weighted spaces as a special class of partial metric spaces derived from an auxiliary weight function. Developing a new area of application, we model deterministic Petri nets as dynamical systems, which we analyse to prove liveness properties of the nets. Generalising to the framework of weighted spaces, we can develop model-independent analytic techniques. To develop a framework in which we can perform the more difficult analysis required for non-deterministic Petri nets, we identify the measure-theoretic aspects of partial metric spaces as fundamental, and use valuations as the link between weight functions and information measures. We are led to develop a notion of local sobriety, which itself appears to be of interest.

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Lazcano, Vanel. „Some problems in depth enhanced video processing“. Doctoral thesis, Universitat Pompeu Fabra, 2016. http://hdl.handle.net/10803/373917.

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In this thesis we tackle two problems, namely, the data interpolation prob- lem in the context of depth computation both for images and for videos, and the problem of the estimation of the apparent movement of objects in image sequences. The rst problem deals with completion of depth data in a region of an image or video where data are missing due to occlusions, unreliable data, damage or lost of data during acquisition. In this thesis we tackle it in two ways. First, we propose a non-local gradient-based energy which is able to complete planes locally. We consider this model as an extension of the bilateral lter to the gradient domain. We have successfully evaluated our model to complete synthetic depth images and also incomplete depth maps provided by a Kinect sensor. The second approach to tackle the problem is an experimental study of the Biased Absolutely Minimizing Lipschitz Extension (biased AMLE in short) for anisotropic interpolation of depth data to big empty regions without informa- tion. The AMLE operator is a cone interpolator, but the biased AMLE is an exponential cone interpolator which makes it more addapted to depth maps of real scenes that usually present soft convex or concave surfaces. Moreover, the biased AMLE operator is able to expand depth data to huge regions. By con- sidering the image domain endowed with an anisotropic metric, the proposed method is able to take into account the underlying geometric information in order not to interpolate across the boundary of objects at di erent depths. We have proposed a numerical model to compute the solution of the biased AMLE which is based on the eikonal operators. Additionally, we have extended the proposed numerical model to video sequences. The second problem deals with the motion estimation of the objects in a video sequence. This problem is known as the optical ow computation. The Optical ow problem is one of the most challenging problems in computer vision. Traditional models to estimate it fail in presence of occlusions and non-uniform illumination. To tackle these problems we proposed a variational model to jointly estimate optical ow and occlusion. Moreover, the proposed model is able to deal with the usual drawback of variational methods in dealing with fast displacements of objects in the scene which are larger than the object it- self. The addition of a term that balance gradient and intensities increases the robustness to illumination changes of the proposed model. The inclusions of a supplementary matches given by exhaustive search in speci cs locations helps to follow large displacements.
En esta tesis se abordan dos problemas: interpolación de datos en el contexto del cálculo de disparidades tanto para imágenes como para video, y el problema de la estimación del movimiento aparente de objetos en una secuencia de imágenes. El primer problema trata de la completación de datos de profundidad en una región de la imagen o video dónde los datos se han perdido debido a oclusiones, datos no confiables, datos dañados o pérdida de datos durante la adquisición. En esta tesis estos problemas se abordan de dos maneras. Primero, se propone una energía basada en gradientes no-locales, energía que puede (localmente) completar planos. Se considera este modelo como una extensión del filtro bilateral al dominio del gradiente. Se ha evaluado en forma exitosa el modelo para completar datos sintéticos y también mapas de profundidad incompletos de un sensor Kinect. El segundo enfoque, para abordar el problema, es un estudio experimental del biased AMLE (Biased Absolutely Minimizing Lipschitz Extension) para interpolación anisotrópica de datos de profundidad en grandes regiones sin información. El operador AMLE es un interpolador de conos, pero el operador biased AMLE es un interpolador de conos exponenciales lo que lo hace estar más adaptado a mapas de profundidad de escenas reales (las que comunmente presentan superficies convexas, concavas y suaves). Además, el operador biased AMLE puede expandir datos de profundidad a regiones grandes. Considerando al dominio de la imagen dotado de una métrica anisotrópica, el método propuesto puede tomar en cuenta información geométrica subyacente para no interpolar a través de los límites de los objetos a diferentes profundidades. Se ha propuesto un modelo numérico, basado en el operador eikonal, para calcular la solución del biased AMLE. Adicionalmente, se ha extendido el modelo numérico a sequencias de video. El cálculo del flujo óptico es uno de los problemas más desafiantes para la visión por computador. Los modelos tradicionales fallan al estimar el flujo óptico en presencia de oclusiones o iluminación no uniforme. Para abordar este problema se propone un modelo variacional para conjuntamente estimar flujo óptico y oclusiones. Además, el modelo propuesto puede tolerar, una limitación tradicional de los métodos variacionales, desplazamientos rápidos de objetos que son más grandes que el tamaño objeto en la escena. La adición de un término para el balance de gradientes e intensidades aumenta la robustez del modelo propuesto ante cambios de iluminación. La inclusión de correspondencias adicionales (obtenidas usando búsqueda exhaustiva en ubicaciones específicas) ayuda a estimar grandes desplazamientos.

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Sebastianutti, Marco. „Geodesic motion and Raychaudhuri equations“. Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18755/.

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The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given space-time, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given space-time must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given space-time. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given space-time, like expansion, shear and twist parameters govern the focusing or de-focusing of geodesic congruences. Physical requirements on matter stress-energy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the Hawking-Penrose singularity theorems.

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„On completeness of partial metric spaces, symmetric spaces and some fixed point results“. Thesis, 2016. http://hdl.handle.net/10500/23206.

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The purpose of the thesis is to study completeness of abstract spaces. In particular, we study completeness in partial metric spaces, partial metric type spaces, dislocated metric spaces, dislocated metric type spaces and symmetric spaces that are generalizations of metric spaces. It is well known that complete metric spaces have a wide range of applications. For instance, the classical Banach contraction principle is phrased in the context of complete metric spaces. Analogously, the Banach's xed point theorem and xed point results for Lipschitzian maps are discussed in this context, namely in, partial metric spaces and metric type spaces. Finally, xed point results are presented for symmetric spaces
Mathematical Sciences
Ph. D. (Mathematics)

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Aphane, Maggie. „On completeness of partial metric spaces, symmetric spaces and some fixed point results“. Thesis, 2016. http://hdl.handle.net/10500/23223.

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Lin, Chung-Yu, und 林重佑. „Fixed point of cyclic weak contractions in partial metric spaces“. Thesis, 2013. http://ndltd.ncl.edu.tw/handle/14107934311591240161.

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碩士
國立新竹教育大學
應用數學系碩士班
101
The purpose of this paper is to study a fixed point theorem for a mapping satisfying the cyclical generalized contractive conditions based on four functions φ,ϕ,ξ：R^+→R^+ and ψ：R^(+^4 )→R^+ in complete partial metric spaces.Our results generalize and improve many recent fixed point theorems in the literature.

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Wei, Ting-Yu, und 魏廷宇. „Fixed point theorems for weak contractions on partial Hausdorff metric spaces“. Thesis, 2017. http://ndltd.ncl.edu.tw/handle/n46p3n.

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碩士
國立清華大學
應用數學系所
105
The purpose of this paper is to study two new fixed point theorems for multi-valued mappings concerning the Meir-Keeler type functions and Rfunctions with respect to the partial Hausdorff metric Hp in completepartial metric spaces. Our results generalize and improve many recent fixed point theorems for the partial Hausdorff metric in the literature.

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Bücher zum Thema "Partial Metric Spaces"

Simovici, Dan A. Mathematical tools for data mining: Set theory, partial orders, combinatorics. London: Springer, 2014.

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Simovici, Dan A. Mathematical tools for data mining: Set theory, partial orders, combinatorics. London: Springer, 2008.

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O'Neill, Simon John. A fundamental study into the theory and application of the partial metric spaces. [s.l.]: typescript, 1998.

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Nicola, Gigli, Savaré Giuseppe, Struwe Michael 1955- und SpringerLink (Online service), Hrsg. Gradient Flows: In Metric Spaces and in the Space of Probability Measures. Basel: Birkhäuser Basel, 2008.

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Pascal, Auscher, Coulhon T und Grigoryan A, Hrsg. Heat kernels and analysis on manifolds, graphs, and metric spaces: Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France. Providence, R.I: American Mathematical Society, 2003.

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Gilles, Lebeau, Hrsg. The hypoelliptic Laplacian and Ray-Singer metrics. Princeton, NJ: Princeton Univeristy Press, 2008.

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1968-, Dafni Galia Devora, McCann Robert John 1968- und Stancu Alina 1968-, Hrsg. Analysis and geometry of metric measure spaces: Lecture notes of the 50th Séminaire de Mathématiques Supérieures (SMS), Montréal, 2011. Providence, Rhode Island, USA: American Mathematical Society, 2013.

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Metric methods for analyzing partially ranked data. Berlin: Springer-Verlag, 1985.

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Critchlow, Douglas E. Metric methods for analyzing partially ranked data. New York: Springer-Verlag, 1985.

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Complex Monge-Ampère equations and geodesics in the space of Kähler metrics. Berlin: Springer Verlag, 2012.

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Buchteile zum Thema "Partial Metric Spaces"

Kirk, William, und Naseer Shahzad. „Partial Metric Spaces“. In Fixed Point Theory in Distance Spaces, 141–52. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10927-5_14.

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Amer, Fariha Jumaa. „Fuzzy Partial Metric Spaces“. In Springer Proceedings in Mathematics & Statistics, 153–61. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28443-9_11.

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Minirani, S., und Sunil Mathew. „Fractals in Partial Metric Spaces“. In Fractals, Wavelets, and their Applications, 203–15. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08105-2_13.

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Minirani, S. „n-Fractals in Partial Metric Spaces“. In Advances in Intelligent Systems and Computing, 529–34. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8061-1_43.

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Güner, Elif, und Halis Aygün. „On Strong Fuzzy Partial Metric Spaces“. In Springer Proceedings in Mathematics & Statistics, 253–66. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-49218-1_18.

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Karapınar, Erdal, und Ravi P. Agarwal. „Fixed Point Theorems in Partial Metric Spaces“. In Synthesis Lectures on Mathematics & Statistics, 97–121. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-14969-6_6.

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Mirdamadi, Fahimeh, Hossein Monfared, Mehdi Asadi und Hossein Soleimani. „Discontinuity at Fixed Point Over Partial Metric Spaces“. In Soft Computing and Optimization, 193–99. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-6406-0_15.

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Karapınar, Erdal, Kenan Taş und Vladimir Rakočević. „Advances on Fixed Point Results on Partial Metric Spaces“. In Nonlinear Systems and Complexity, 3–66. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91065-9_1.

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Antoine, Jean-Pierre, und Camillo Trapani. „Metric Operators, Generalized Hermiticity, and Partial Inner Product Spaces“. In STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, 1–20. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-97175-9_1.

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Matthews, Steve, und Michael Bukatin. „An Intelligent Theory of Cost for Partial Metric Spaces“. In Artificial General Intelligence, 168–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-35506-6_18.

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Konferenzberichte zum Thema "Partial Metric Spaces"

Ozturk, Vildan, und Duran Turkoglu. „Integral type contractions in partial metric spaces“. In CURRENT TRENDS IN RENEWABLE AND ALTERNATE ENERGY. Author(s), 2019. http://dx.doi.org/10.1063/1.5095116.

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Tiwari, Shiv Kant, Laxmi Rathour, Suresh Kumar Sahani und Lakshmi Narayan Mishra. „Results for coupled fixed point theorems in partial order metric spaces“. In 1ST INTERNATIONAL CONFERENCE ON COMPUTATIONAL APPLIED SCIENCES & IT’S APPLICATIONS. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0149509.

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Aslantas, Mustafa, und Ali Hüssein Bachay. „Periodic point results for Boyd-Wong contraction mappings on partial metric spaces“. In FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0042310.

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Bachay, Ali Hussein, und Mustafa Aslantas. „Periodic point results via Bianchini-Grandolfi gauge functions on partial metric spaces“. In PROCEEDING OF THE 1ST INTERNATIONAL CONFERENCE ON ADVANCED RESEARCH IN PURE AND APPLIED SCIENCE (ICARPAS2021): Third Annual Conference of Al-Muthanna University/College of Science. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0093612.

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Rathee, Savita, und Neelam Kumari. „Fixed point theorems of operators with PPF dependence in partial b-metric spaces“. In INTERNATIONAL CONFERENCE ON ADVANCES IN MULTI-DISCIPLINARY SCIENCES AND ENGINEERING RESEARCH: ICAMSER-2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0095811.

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Das, Dipankar, Babla Chandra Ghosh und Vishnu Narayan Mishra. „Fixed point results via G-class function in ordered dualistic partial metric spaces“. In 1ST INTERNATIONAL CONFERENCE ON COMPUTATIONAL APPLIED SCIENCES & IT’S APPLICATIONS. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0148389.

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Anuradha und Seema Mehra. „Fixed point results using implicit relation on partial b-metric spaces endowed with a graph“. In DIDACTIC TRANSFER OF PHYSICS KNOWLEDGE THROUGH DISTANCE EDUCATION: DIDFYZ 2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0081146.

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Adilakshmi, G., und G. N. V. Kishore. „A new approach of finding fixed point results in partial metric spaces and applications to graph theory“. In CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS IN ENGINEERING: CMSAE-2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0149113.

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Esi, Ayten, Esen Hanaç und Ayhan Esi. „Difference convergence on partial metric space“. In CURRENT TRENDS IN RENEWABLE AND ALTERNATE ENERGY. Author(s), 2019. http://dx.doi.org/10.1063/1.5095101.

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Wang, Changchun, Zhiyou Chen und Jie Ran. „Some Fixed Point Theorems in Partial Cone Metric Space“. In 2019 6th International Conference on Information Science and Control Engineering (ICISCE). IEEE, 2019. http://dx.doi.org/10.1109/icisce48695.2019.00119.

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Berichte der Organisationen zum Thema "Partial Metric Spaces"

Tawfik, Aly, Deify Law, Juris Grasis, Joseph Oldham und Moe Salem. COVID-19 Public Transportation Air Circulation and Virus Mitigation Study. Mineta Transportation Institute, Juni 2022. http://dx.doi.org/10.31979/mti.2021.2036.

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COVID-19 may have forever changed our world. Given the limited space and air circulation, potential infections on public transportation could be concerningly high. Accordingly, this study has two objectives: (1) to understand air circulation patterns inside the cabins of buses; and (2) to test the impact of different technologies in mitigating viruses from the air and on surfaces inside bus cabins. For the first objective, different devices, metrics and experiments (including colored smoke; videotaping; anemometers; pressure differentials; particle counts; and 3D numerical simulation models) were utilized and implemented to understand and quantify air circulation inside different buses, with different characteristics, and under different operating conditions (e.g. with windows open and shut). For the second objective, three different live prokaryotic viruses were utilized: Phi6, MS2 and T7. Various technologies (including positive pressure environment inside the cabin, HEPA filters with different MERV ratings, concentrated UV exposure with charged carbon filters in the HVAC systems, center point photocatalytic oxidation technology, ionization, and surface antiviral agents) were tested to evaluate the potential of mitigating COVID-19 infections via air and surfaces in public transportation. The effectiveness of these technologies on the three live viruses was tested in both the lab and in buses in the field. The results of the first objective experiments indicated the efficiency of HVAC system designs, where the speed of air spread was consistently much faster than the speed of air clearing. Hence, indicating the need for additional virus mitigation from the cabin. Results of the second objective experiments indicated that photocatalytic oxidation inserts and UVC lights were the most efficient in mitigating viruses from the air. On the other hand, positive pressure mitigated all viruses from surfaces; however, copper foil tape and fabrics with a high percentage of copper mitigated only the Phi6 virus from surfaces. High-temperature heating was also found to be highly effective in mitigating the different viruses from the vehicle cabin. Finally, limited exploratory experiments to test possible toxic by-products of photocatalytic oxidation and UVC lights inside the bus cabin did not detect any increase in levels of formaldehyde, ozone, or volatile organic compounds. Implementation of these findings in transit buses, in addition to the use of personal protective equipment, could be significantly valuable for protection of passengers and drivers on public transportation modes, possibly against all forms of air-borne viruses.

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