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The second denominator is strictly positive because b < M /Al. The right side of Equation (4.13) is equal to zero, if pw Aw (M bAl ) pl Al (M + bAw ) = 0. This results in the optimal equation for b: b* = ((pw Aw pl Al ) / (pw Aw + plAw )) M /Al = ((pw Aw pl Al ) /Aw ) M /Al = (pw (1 pw )Al /Aw ) M /Al

Statically allocated data. Consider Figure 5.2. Here, a statically allocated array password is adjacent to an int variable passvalid, which stores the outcome of a password validity check. The password validity check will set passvalid to 1 (TRUE) if the user password is correct and will leave the field untouched otherwise. The user input to the field password can be carefully chosen to overwrite passvalid with a 1 even though the password validity check fails. If the program does not check for overflows on reading input into the password field, a hacker may be allowed access. Dynamically allocated data. The program heap allocates and de-allocates dynamic memory through system calls (such as malloc( ) and free( ) in C). Overwriting dynamic memory has fewer negative consequences because dynamic memory is not used for execution, i.e. the instruction pointer of the program is never set from the contents of dynamic memory. We also, in general, cannot guarantee an exact relative location of two dynamically allocated segments. In this situation, overrunning the first segment cannot precisely target the second. However,

default: break; }//end switch (wMsg) return FALSE; } BOOL CALLBACK HKeyN2ValuesDlg(HWND hDlg, UINT message, WPARAM wParam, LPARAM lParam) { HWND hWndList; INT i = 0, rc, iTest; DWORD dwNSize; DWORD dwDSize; DWORD dwType; DWORD dwDatum; TCHAR szName[32]; HKEY hKeyN2; BYTE bData[26]; BYTE bBuffer[48]; switch (message) { case WM_INITDIALOG: hWndList = GetDlgItem(hDlg,IDC_VALUE_LIST ); //open key to gain access to values rc = RegOpenKeyEx (HKEY_LOCAL_MACHINE, TEXT ( Software\\n2 ), 0, KEY_ENUMERATE_SUB_KEYS , &hKeyN2); if (rc != ERROR_SUCCESS) {return FALSE;} //set up to enumerate values dwNSize = dim(szName); dwDSize = sizeof(bData); rc = RegEnumValue(hKeyN2, i, szName, &dwNSize, NULL, &dwType, (PBYTE)&bData, &dwDSize ); while (rc == ERROR_SUCCESS) { ListBox_InsertString(hWndList, -1, szName); //distinguish between key types memset( bBuffer, 0x0, sizeof(bBuffer)); if( dwType == REG_BINARY ) { wsprintf( (LPTSTR)&bBuffer,TEXT( %s Data:%x ), TEXT( REG_BINARY ), *bData ); } if( dwType == REG_DWORD ) { dwDatum = (DWORD)(bData); iTest = (int)dwDatum;

thank Janet Aromando, Mike Boaz, Jeff Bramley, Terry Cleary, Dave Cura, Bryon Donahue, Irwin Dunietz, John Eddy, Neal Fildes, Cindy Flaspohler, Tim Frommeyer, Don Gerth, Doug Ginn, Abhay Jain, Steve Meyer, Mike Newbury, Randy Ringeisen, Hans Ros, Ray Sandfoss, George Schwerdtman, Manoucher Shahrava, Mohammed Shakir, David Simen, Anoop Singhal, David Timidaiski, Tim Velten, and Dave Williamson. Special thanks go to many friends and their families for countless hours over two decades spent debating all things under the sun, some of which related to computing and engineering. I thank Pankaj Agarwal, Alok Baveja, Paolo Bucci, Jai and Veena Chhugani, Anil and Punam Goel, Nilendu and Urmila Gupta, Nirmala Iyer, Aarati Kanekar, Atul and Manu Khare, K. Ananth Krishnan, Asish and Anandi Law, Pushkal Pandey, Sushant and Susan Patnaik, Mahendra Ramachandran, Ming Jye-Sheu, and Manoj and Neeta Tandon for their friendship. This book would not exist but for my family. I thank my family, Jayashree, Akhila and Madhavan, Bhaskar and Vidyut, and especially Amma, Appa, Aai, and Daiyya for their blessings. Without their confidence, support, and help in so many ways, I could not have attempted let alone completed this task. Hats off to you all. To Ronak and Mallika, for their patience and humor, and last but not least, to Beena, for all the support in the world. You steered the ship through the storm while the first mate was down in the bilge thinking this book up. This book is for you.

30. u(P11) u(P22) u(P33) 35, u(P21) u(P32) 20, u(P31) 10, u(P12) u(P23) 50, u(P13) 60 32. u(P21) 500, u(P22) 200, u 100 at all other gridpoints 36. From the 3D-values given below we see that at each point x 0 the temperature oscillates with a phase lag and a maximum amplitude that decreases with decreasing x.

//set up to enumerate values dwNSize = dim(szName); dwDSize = sizeof(bData);

Check that email messages are sent to the appropriate customers, in other words, those who had loans that were due back in four days or less: Anthony, Tom, and Harry. Check also that the email messages refer to the correct loans.

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