As defined by Blake-Wilson & Menezes (1999), an unknown key-share (UKS) attack on an authenticated key agreement (AK) or authenticated key agreement with key confirmation (AKC) protocol is an attack whereby an entity A {\displaystyle A} ends up believing she shares a key with B {\displaystyle B} , and although this is in fact the case, B {\displaystyle B} mistakenly believes the key is instead shared with an entity E ≠ A {\displaystyle E\neq A} . In other words, in a UKS, an opponent, say Eve, coerces honest parties Alice and Bob into establishing a secret key where at least one of Alice and Bob does not know that the secret key is shared with the other. For example, Eve may coerce Bob into believing he shares the key with Eve, while he actually shares the key with Alice. The “key share” with Alice is thus unknown to Bob.
InciWeb
InciWeb is an interagency all-risk incident web information management system provided by the United States Forest Service released in 2004. It was originally developed for wildland fire emergencies, but can be also used for other emergency incidents (natural disasters, such as earthquakes, floods, hurricanes, and tornadoes). == Introduction == It was developed with two primary missions: 1. Provide the public a single source of incident related information 2. Provide a standardized reporting tool for the Public Affairs community Official announcements include evacuations, road closures, news releases, maps, photographs, and basic info and current situation about the incident. Incident information can be accessed by: web browser at https://inciweb.wildfire.gov/ Twitter RSS web feed == Technical == The original application was hosted at the United States Forest Service - Wildland Fire Training and Conference Center, at McClellan Airfield, California, comprising three servers: Database server Administrative server Load balancer for the public content which routes traffic to a pool of eight servers. Web traffic averages 2 million plus hits daily during the fire season with the ability to handle 3.5 million hits. The servers were moved to the National information Technology Center (NITC), Kansas City, Missouri on July 16, 2008, along with the release of version 2.0; the current version is 2.2. == Availability issues == InciWeb was having technical difficulties due to the high volume of Internet users trying to access the site during the September–October 2006 Day Fire and the Summer 2008 California wildfires. == Participating agencies == United States Forest Service Bureau of Land Management Bureau of Indian Affairs Fish and Wildlife Service National Park Service National Oceanic & Atmospheric Administration Department of the Interior Office of Aircraft Services National Association of State Foresters United States Fire Administration These same agencies are also in the National Interagency Fire Center.
Artipic
Artipic is a graphics editor developed for Microsoft Windows. An older version for macOS is still available but unsupported. Artipic features drawing, editing, retouching, transforming and composing images including color corrections, effects and layer-based operations. It converts all common image formats and imports camera raw formats. In the global image editing ecosystem Artipic can be positioned somewhere in the middle. It differs from simple free photo editors by more advanced capabilities, however it does not cover the complete professional-level functionality pack provided by industry leaders like Adobe Photoshop. == History == Artipic developed by Swedish company Artipic AB. Artipic 1.0 was released in March 2014 as a free version. The first commercial version on Microsoft Windows was released in November 2014, on macOS – in October 2015. == Features == Supports Microsoft Windows and macOS Standard tools: select, crop, move, rotate, transform, stamp, color picking, text Advanced tools: custom brushes, gradients, shapes, paths, layers and masks Special tools: healing brush, red-eye effect reduction, dodge and burn brushes Adjustments: Brightness & Contrast, Hue & Saturation, Curves, Levels, Color Balance, Gamma Correction, Exposure, Color Temperature, Tint, Color Enhancer, Photo Filter Simulation, Posterization, Thresholding Filters: Smoothen, Sharpen, Vignetting, High-pass, Diffuse Glow, Shadow, Gaussian Blur Reversible (non-destructive) stylization presets Batch processing White balance RAW-converter including Gray Card Adobe Photoshop images supported == Version history ==
International Speech Communication Association
The International Speech Communication Association (ISCA) is a non-profit organization and one of the two main professional associations for speech communication science and technology, the other association being the IEEE Signal Processing Society. == Purpose == The purpose of the International Speech Communication Association (ISCA) is to promote the study and application of automatic speech processing, including speech recognition and synthesis, as well as related areas such as speaker recognition and speech compression. The association's activities cover all aspects of speech processing, including computational, linguistic, and theoretical aspects. The primary goal of the International Speech Communication Association (ISCA) is to advance the field of automatic speech processing and communication technology through research, education, and collaboration. By promoting the study and application of speech technologies such as speech recognition, speech synthesis, speaker recognition, and speech compression, ISCA aims to foster innovation and development in the areas of human-computer interaction, telecommunications, and multimedia applications. ISCA serves as a platform for researchers, academics, industry professionals, and students to exchange knowledge, share best practices, and foster interdisciplinary dialogue in the field of speech communication science. Through conferences, workshops, publications, and educational initiatives, ISCA seeks to enhance the understanding of speech processing mechanisms, improve the accuracy and efficiency of speech technologies, and explore new frontiers in the realm of human language communication. Furthermore, ISCA plays a crucial role in promoting international collaboration and networking among professionals in the speech communication community. By facilitating partnerships and cooperation between individuals and organizations worldwide, ISCA seeks to drive global progress in speech technology research and application, ultimately contributing to the advancement of communication systems, accessibility tools, and interactive interfaces that benefit society as a whole. == Conferences == ISCA organizes yearly the Interspeech conference. Most recent Interspeech: 2013 Lyon, France 2014 Singapore 2015 Dresden, Germany 2016 San Francisco, US 2017 Stockholm, Sweden 2018 Hyderabad, India 2019 Graz, Austria 2020 Shanghai, China (fully virtual) 2021 Brno, Czechia (hybrid) 2022 Incheon, South Korea 2023 Dublin, Ireland 2023 Kos Island, Greece Forthcoming Interspeech: 2025 Rotterdam, the Netherlands == ISCA board == The ISCA president for 2023-2025 is Odette Scharenborg. The vice president is Bhuvana Ramabhadran and the other members are professionals in the field. == History of ISCA == The precursor to Interspeech was a conference called Eurospeech, first held in 1989 and organised by Jean-Pierre Tubach. It was the conference of the European Speech Communication Association (ESCA), itself the precursor of the International Speech Communication Association (ISCA). A year later another conference on speech science and technology was started: the International Conference on Spoken Language Processing (ICSLP), which was founded in 1990 by Hiroya Fujisaki. The first ISCA (vs. ESCA) event was the merging of Eurospeech and ICSLP to create ICSLP-Interspeech, held in Beijing, China in 2000. This was followed by Eurospeech-Interspeech, which was held in Aalborg, Denmark in 2001. In 2007, the Eurospeech and ICSLP parts of the conference names were dropped and Interspeech became the name of the yearly conference (first Interspeech location: Antwerp, Belgium).
Manual override
A manual override (MO) or manual analog override (MAO) is a mechanism where control is taken from an automated system and given to the user. For example, a manual override in photography refers to the ability for the human photographer to turn off the automatic aperture sizing, automatic focusing, or any other automated system on the camera. Some manual overrides can be used to veto an automated system's judgment when the system is in error. An example of this is a printer's ink level detection: in one case, a researcher found that when he overrode the system, up to 38% more pages could be printed at good quality by the printer than the automated system would have allowed. Automated systems are becoming increasingly common and integrated into everyday objects such as automobiles and domestic appliances. This development of ubiquitous computing raises general issues of policy and law about the need for manual overrides for matters of great importance such as life-threatening situations and major economic decisions. The loyalty of such autonomous devices then becomes an issue. If they follow rules installed by the manufacturer or required by law and refuse to cede control in some situations then the owners of the devices may feel disempowered, alienated and lacking true ownership. == Major incidents == China Airlines Flight 140 crashed, causing many deaths, due to a misunderstanding about the manual overrides for the autopilot. The Take-Off/Go Around system had been activated to abort a landing. It was programmed to ignore manual controls in this situation but the human pilots tried to continue the landing. The conflicting control signals from the pilots and autopilot then resulted in the aircraft stalling and crashing. The autopilot for this aircraft type was then reprogrammed so that it would never ignore a manual override.
List of C software and tools
This is a list of software and programming tools for the C programming language, including libraries, debuggers, compilers, integrated development environments (IDEs), and other related development tools and utilities. == Libraries and tools == Adns — asynchronous DNS resolver library Advanced Linux Sound Architecture — API for sound card device drivers Allegro — cross-platform software library for video game development Apache Portable Runtime — Apache web server tool set of APIs that map to the underlying operating system Argon2 — memory-hard password hashing library Berkeley DB — embedded database software library for key/value data Binary File Descriptor library — binary file manipulation library in the GNU toolchain Boehm garbage collector – conservative garbage collector Borland Graphics Interface — graphics library for Borland compilers BSAFE — FIPS 140-2 validated cryptography library Chipmunk — 2D real-time rigid body physics engine C POSIX library — specification of a C standard library for POSIX systems C standard library – standard library for the C programming language Cairo – vector graphics library API for software developers CFD General Notation System (CGNS) — data format and library for computational fluid dynamics cJSON — lightweight JSON parser CLIPS — public-domain software tool for building expert systems Core Audio — low-level API for dealing with sound in Apple's macOS and iOS operating systems Core Foundation — API for macOS and iOS and other Apple operating systems Core Image — GPU accelerated image processing technology for Apple operating systems with Quartz graphics rendering layer. Core Text — text layout and font rendering API for macOS and iOS. Cryptlib — portable cryptography library cURL / libcurl — CLI app for uploading and downloading individual files, such as a URL from a web server over HTTP. DevIL — cross-platform image library for loading and converting file formats DirectFB — graphics acceleration and input device handling library Dld — dynamic loading library Expat — stream-oriented XML 1.0 parser library, written in C99. FFmpeg — multimedia framework for audio/video processing Fontconfig — font customization and configuration library FreeTDS — database library for Sybase and Microsoft SQL Server FreeType — render text onto bitmaps with a font rasterization engine GD Graphics Library — image creation and manipulation library GDK — graphics abstraction layer for GTK GEGL — graph-based image processing framework GIO — I/O and virtual file system library in GLib GLib — utility library providing data structures, event loops, and portability functions. glibc — GNU implementation of the C standard library GLFW — library for OpenGL contexts, windows, and input device handling GNet — networking library for GLib GNU Libtool — Library management tool GNU portability library — collection of portability routines for GNU software GNU Portable Threads — POSIX/ANSI-C based user space thread library for UNIX for scheduling multithreading GNU Readline — command-line editing library GnuTLS — secure communications (TLS/SSL) library GObject — object system library for GNOME GTK — widget toolkit for creating graphical user interfaces GTK Scene Graph Kit (GSK) — scene graph and rendering toolkit for GTK HDF — file format and library for managing large datasets Integrated Performance Primitives — Intel library of optimized multimedia and data processing routines IUP — portable GUI toolkit J2K-Codec — JPEG 2000 image codec JasPer — reference implementation of the codec specified in the JPEG-2000 Part-1 standard LDAP API — API for interacting with Lightweight Directory Access Protocol LZO — lossless compression library Liba52 — decoder for A/52 (AC-3) audio streams libarchive — reading and writing various archive and compression formats Libart — 2D graphics library Libavcodec — codec library from FFmpeg Libavdevice — library for handling multimedia devices Libavfilter — audio and video filter library Libavformat — library for muxing and demuxing multimedia Libpcap — packet capture library Libdca — decoder for DTS audio Libdvdcss — access to encrypted DVD-Video discs libevent — asynchronous event notification callbacks libffi — foreign function interface libfuse — userspace filesystem Libgegl — programming interface to GEGL image processing libgcrypt — cryptography Libgimp — plug-in development library for GIMP Libhybris — compatibility layer for running Android libraries on Linux Libinput — input device library for Wayland and X.Org libjpeg — JPEG image library libLAS — reading and writing geospatial data encoded in the ASPRS laser (LAS) file format libmicrohttpd — small C library for embedding HTTP server functionality Libmpcodecs — media player codec library from MPlayer Libmpdemux — demultiplexing library from MPlayer libpng — PNG image format Libpostproc — video post-processing library from FFmpeg libpq — PostgreSQL client LibreSSL — fork of OpenSSL for TLS Librsb — parallel library for sparse matrix computations Librsvg — SVG rendering library libsndfile — reading and writing audio files libsodium — easy-to-use cryptography library Libswscale — image scaling and colorspace conversion library LibTIFF — TIFF image handling library Libusb — USB device access library Libuv — asynchronous I/O and event loop library LibVLC — media player engine from VLC LibVNCServer — implementation of the VNC server protocol Libvpx — VP8 and VP9 video codec library Libwww — early World Wide Web protocol library from W3C libxml2 — XML parsing Libxslt — XSLT library for the GNOME Project libzip — ZIP archives Lightning Memory-Mapped Database — fast key–value database engine LittleCMS — open-source color management system LZ4 — fast lossless compression algorithm LZFSE — compression library developed by Apple MatrixSSL — lightweight TLS implementation Mbed TLS — portable cryptography and TLS library MediaLib — Sun Microsystems library for multimedia processing Mesa — OpenGL and Vulkan graphics library Microwindows — small windowing system for embedded devices Ming — library for generating SWF (Flash) files Mongoose — embedded web server and networking library Mpg123 — MP3 audio decoding library MPIR — multiple-precision arithmetic library MsQuic — Microsoft implementation of the QUIC transport protocol MuJoCo — physics engine for robotics and control Mustache — logic-less templating library Ncurses — terminal control library Nettle — low-level cryptography library Newt — text-based user interface library Netpbm — graphics conversion and processing library Nghttp2 — implementation of the HTTP/2 protocol Oniguruma — regular expression library Open Asset Import Library — library to import/export 3D model formats OpenCL — parallel computing API/library OpenCV — computer vision OpenGL — API for rendering 2D and 3D vector graphics OpenGL Utility Library — OpenGL utility functions OpenJPEG — JPEG 2000 image codec OpenSSL — SSL and TLS protocols and cryptography library Pango — layout engine library which works with the HarfBuzz shaping engine for displaying multi-language text perf (Linux) — performance analyzing tool PCRE — regular expression library PROJ — library for map projections and coordinate transforms Quartz 2D — 2D graphics rendering API for macOS and iOS platforms, part of the Core Graphics framework. Raylib — simple library for games and multimedia Redland RDF Application Framework — RDF data storage library S2n-tls — TLS implementation from AWS Setcontext — context switching library functions SDL — Simple DirectMedia Layer systemd — system and service manager libraries for Linux Tk — GUI widgets for building graphical user interfaces VDPAU — video decoding acceleration API Vorbis — audio compression codec library VTD-XML — high-performance XML parser Wimlib — library for handling Windows Imaging Format disk images Windows.h — base Windows API header file WolfSSH — lightweight SSH library WolfSSL — lightweight SSL/TLS library X Toolkit Intrinsics — toolkit library for the X Window System x264 — H.264 video codec library XCB — C binding for the X Window System protocol Xft — font rendering library using FreeType Xlib — low-level X Window System API XMDF — eXtensible Model Data Format for scientific data XMLStarlet — XML command-line toolkit zlib — data compression Zopfli — data compression library that performs deflate, gzip and zlib data encoding. Zstd — fast data compression library == Integrated development environments == Anjuta — GNOME IDE CLion — cross-platform commercial IDE from JetBrains Code::Blocks — cross-platform open-source IDE CodeLite — open-source IDE Dev-C++ Eclipse CDT Geany — text editor with IDE features KDevelop — KDE IDE NetBeans Qt Creator SlickEdit Visual Studio Xcode === Online IDEs === CodeSandbox — online IDE primarily for web development with some C support via containers GitHub Codespaces — cloud-based online IDE developed by GitHub Google Cloud Shell — browser-based shell and editor that can comp
Spherical basis
In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. While spherical polar coordinates are one orthogonal coordinate system for expressing vectors and tensors using polar and azimuthal angles and radial distance, the spherical basis are constructed from the standard basis and use complex numbers. == In three dimensions == A vector A in 3D Euclidean space R3 can be expressed in the familiar Cartesian coordinate system in the standard basis ex, ey, ez, and coordinates Ax, Ay, Az: or any other coordinate system with associated basis set of vectors. From this extend the scalars to allow multiplication by complex numbers, so that we are now working in C 3 {\displaystyle \mathbb {C} ^{3}} rather than R 3 {\displaystyle \mathbb {R} ^{3}} . === Basis definition === In the spherical bases denoted e+, e−, e0, and associated coordinates with respect to this basis, denoted A+, A−, A0, the vector A is: where the spherical basis vectors can be defined in terms of the Cartesian basis using complex-valued coefficients in the xy plane: in which i {\displaystyle i} denotes the imaginary unit, and one normal to the plane in the z direction: e 0 = e z {\displaystyle \mathbf {e} _{0}=\mathbf {e} _{z}} The inverse relations are: === Commutator definition === While giving a basis in a 3-dimensional space is a valid definition for a spherical tensor, it only covers the case for when the rank k {\displaystyle k} is 1. For higher ranks, one may use either the commutator, or rotation definition of a spherical tensor. The commutator definition is given below, any operator T q ( k ) {\displaystyle T_{q}^{(k)}} that satisfies the following relations is a spherical tensor: [ J ± , T q ( k ) ] = ℏ ( k ∓ q ) ( k ± q + 1 ) T q ± 1 ( k ) {\displaystyle [J_{\pm },T_{q}^{(k)}]=\hbar {\sqrt {(k\mp q)(k\pm q+1)}}T_{q\pm 1}^{(k)}} [ J z , T q ( k ) ] = ℏ q T q ( k ) {\displaystyle [J_{z},T_{q}^{(k)}]=\hbar qT_{q}^{(k)}} === Rotation definition === Analogously to how the spherical harmonics transform under a rotation, a general spherical tensor transforms as follows, when the states transform under the unitary Wigner D-matrix D ( R ) {\displaystyle {\mathcal {D}}(R)} , where R is a (3×3 rotation) group element in SO(3). That is, these matrices represent the rotation group elements. With the help of its Lie algebra, one can show these two definitions are equivalent. D ( R ) T q ( k ) D † ( R ) = ∑ q ′ = − k k T q ′ ( k ) D q ′ q ( k ) {\displaystyle {\mathcal {D}}(R)T_{q}^{(k)}{\mathcal {D}}^{\dagger }(R)=\sum _{q'=-k}^{k}T_{q'}^{(k)}{\mathcal {D}}_{q'q}^{(k)}} === Coordinate vectors === For the spherical basis, the coordinates are complex-valued numbers A+, A0, A−, and can be found by substitution of (3B) into (1), or directly calculated from the inner product ⟨, ⟩ (5): A 0 = ⟨ e 0 , A ⟩ = ⟨ e z , A ⟩ = A z {\displaystyle A_{0}=\left\langle \mathbf {e} _{0},\mathbf {A} \right\rangle =\left\langle \mathbf {e} _{z},\mathbf {A} \right\rangle =A_{z}} with inverse relations: In general, for two vectors with complex coefficients in the same real-valued orthonormal basis ei, with the property ei·ej = δij, the inner product is: where · is the usual dot product and the complex conjugate must be used to keep the magnitude (or "norm") of the vector positive definite. == Properties (three dimensions) == === Orthonormality === The spherical basis is an orthonormal basis, since the inner product ⟨, ⟩ (5) of every pair vanishes meaning the basis vectors are all mutually orthogonal: ⟨ e + , e − ⟩ = ⟨ e − , e 0 ⟩ = ⟨ e 0 , e + ⟩ = 0 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{0}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{+}\right\rangle =0} and each basis vector is a unit vector: ⟨ e + , e + ⟩ = ⟨ e − , e − ⟩ = ⟨ e 0 , e 0 ⟩ = 1 {\displaystyle \left\langle \mathbf {e} _{+},\mathbf {e} _{+}\right\rangle =\left\langle \mathbf {e} _{-},\mathbf {e} _{-}\right\rangle =\left\langle \mathbf {e} _{0},\mathbf {e} _{0}\right\rangle =1} hence the need for the normalizing factors of 1 / 2 {\displaystyle 1/\!{\sqrt {2}}} . === Change of basis matrix === The defining relations (3A) can be summarized by a transformation matrix U: ( e + e − e 0 ) = U ( e x e y e z ) , U = ( − 1 2 − i 2 0 + 1 2 − i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}=\mathbf {U} {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}\,,\quad \mathbf {U} ={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} with inverse: ( e x e y e z ) = U − 1 ( e + e − e 0 ) , U − 1 = ( − 1 2 + 1 2 0 + i 2 + i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}\mathbf {e} _{x}\\\mathbf {e} _{y}\\\mathbf {e} _{z}\end{pmatrix}}=\mathbf {U} ^{-1}{\begin{pmatrix}\mathbf {e} _{+}\\\mathbf {e} _{-}\\\mathbf {e} _{0}\end{pmatrix}}\,,\quad \mathbf {U} ^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\+{\frac {i}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} It can be seen that U is a unitary matrix, in other words its Hermitian conjugate U† (complex conjugate and matrix transpose) is also the inverse matrix U−1. For the coordinates: ( A + A − A 0 ) = U ∗ ( A x A y A z ) , U ∗ = ( − 1 2 + i 2 0 + 1 2 + i 2 0 0 0 1 ) , {\displaystyle {\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}=\mathbf {U} ^{\mathrm {} }{\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}\,,\quad \mathbf {U} ^{\mathrm {} }={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\+{\frac {1}{\sqrt {2}}}&+{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,,} and inverse: ( A x A y A z ) = ( U ∗ ) − 1 ( A + A − A 0 ) , ( U ∗ ) − 1 = ( − 1 2 + 1 2 0 − i 2 − i 2 0 0 0 1 ) . {\displaystyle {\begin{pmatrix}A_{x}\\A_{y}\\A_{z}\end{pmatrix}}=(\mathbf {U} ^{\mathrm {} })^{-1}{\begin{pmatrix}A_{+}\\A_{-}\\A_{0}\end{pmatrix}}\,,\quad (\mathbf {U} ^{\mathrm {} })^{-1}={\begin{pmatrix}-{\frac {1}{\sqrt {2}}}&+{\frac {1}{\sqrt {2}}}&0\\-{\frac {i}{\sqrt {2}}}&-{\frac {i}{\sqrt {2}}}&0\\0&0&1\end{pmatrix}}\,.} === Cross products === Taking cross products of the spherical basis vectors, we find an obvious relation: e q × e q = 0 {\displaystyle \mathbf {e} _{q}\times \mathbf {e} _{q}={\boldsymbol {0}}} where q is a placeholder for +, −, 0, and two less obvious relations: e ± × e ∓ = ± i e 0 {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{\mp }=\pm i\mathbf {e} _{0}} e ± × e 0 = ± i e ± {\displaystyle \mathbf {e} _{\pm }\times \mathbf {e} _{0}=\pm i\mathbf {e} _{\pm }} === Inner product in the spherical basis === The inner product between two vectors A and B in the spherical basis follows from the above definition of the inner product: ⟨ A , B ⟩ = A + B + ⋆ + A − B − ⋆ + A 0 B 0 ⋆ {\displaystyle \left\langle \mathbf {A} ,\mathbf {B} \right\rangle =A_{+}B_{+}^{\star }+A_{-}B_{-}^{\star }+A_{0}B_{0}^{\star }}